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Volumn , Issue 550, 2002, Pages 141-167

On certain analogies between knots and primes

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EID: 0036386463     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.2002.070     Document Type: Article
Times cited : (37)

References (67)
  • 1
    • 38249008968 scopus 로고
    • Some cases for Fontaine-Mazur conjecture
    • [Bo]
    • [Bo] N. Boston, Some cases for Fontaine-Mazur conjecture, J. Number Th. 42 (1992), 285-291; II, ibid. 75 (1999), 161-169.
    • (1992) J. Number Th. , vol.42 , pp. 285-291
    • Boston, N.1
  • 2
    • 0000635893 scopus 로고    scopus 로고
    • Some cases for Fontaine-Mazur conjecture, II
    • [Bo] N. Boston, Some cases for Fontaine-Mazur conjecture, J. Number Th. 42 (1992), 285-291; II, ibid. 75 (1999), 161-169.
    • (1999) J. Number Th. , vol.75 , pp. 161-169
  • 3
    • 0001241805 scopus 로고
    • Pseudocompact algebras, profinite groups and class formations
    • [Br]
    • [Br] A. Brumer, Pseudocompact algebras, profinite groups and class formations, J. Algebra 4 (1966), 442470.
    • (1966) J. Algebra , vol.4 , pp. 442470
    • Brumer, A.1
  • 4
    • 84968483705 scopus 로고
    • Commutator calculus and link invariants
    • [C] erratum 993
    • [C] K. T. Chen, Commutator calculus and link invariants, Proc. Amer. Math. Soc. 3 (1954), 44-55 (erratum 993).
    • (1954) Proc. Amer. Math. Soc. , vol.3 , pp. 44-55
    • Chen, K.T.1
  • 5
    • 0002970547 scopus 로고
    • Free differential calculus, IV. The quotient groups of the lower central series
    • [CFL]
    • [CFL] K. T. Chen, R. H. Fox and R. C. Lyndon, Free differential calculus, IV. The quotient groups of the lower central series, Ann. Math. 68 (1958), 81-95.
    • (1958) Ann. Math. , vol.68 , pp. 81-95
    • Chen, K.T.1    Fox, R.H.2    Lyndon, R.C.3
  • 6
    • 0042789350 scopus 로고
    • Corresponding groups and module sequences
    • [C1]
    • [C1] R. H. Crowell, Corresponding groups and module sequences, Nagoya Math. J. 19 (1961), 27-40.
    • (1961) Nagoya Math. J. , vol.19 , pp. 27-40
    • Crowell, R.H.1
  • 7
    • 0010871818 scopus 로고
    • The derived module of a homomorphism
    • [C2]
    • [C2] R. H. Crowell, The derived module of a homomorphism, Adv. Math. 6 (1971), 210-238.
    • (1971) Adv. Math. , vol.6 , pp. 210-238
    • Crowell, R.H.1
  • 8
    • 0003202127 scopus 로고
    • Introduction to knot theory
    • [CF] Ginn, and Co. Boston, Mass., 2nd ed.
    • [CF] R. H. Crowell, R. H. Fox, Introduction to knot theory, Ginn, and Co. Boston, Mass. (1963), 2nd ed. Springer Grad. Texts Math. 57 (1977).
    • (1963) Springer Grad. Texts Math. , vol.57
    • Crowell, R.H.1    Fox, R.H.2
  • 9
    • 0001643481 scopus 로고
    • On the maximal p-extension of a local field
    • [D1]
    • [D1] S. P. Demuškin, On the maximal p-extension of a local field (in Russian), Izv. Akad. Nauk. USSR Math. Ser. 25 (1961), 329-346.
    • (1961) Izv. Akad. Nauk. USSR Math. Ser. , vol.25 , pp. 329-346
    • Demuškin, S.P.1
  • 10
    • 0000528711 scopus 로고
    • On 2-extensions of a local field
    • [D2]
    • [D2] S. P. Demuškin, On 2-extensions of a local field (in Russian), Math. Sib. 4 (1963), 951-955.
    • (1963) Math. Sib. , vol.4 , pp. 951-955
    • Demuškin, S.P.1
  • 12
    • 0002165846 scopus 로고
    • Geometric Galois representations, elliptic curves, modular forms, and format's last theorem
    • [F-M] Hong Kong, Internat. Press, Cambridge, MA
    • [F-M] J.-M. Fontaine and B. Mazur, Geometric Galois representations, Elliptic curves, modular forms, and Format's last theorem (Hong Kong, 1993), Ser. Number Theory, I, Internat. Press, Cambridge, MA (1995), 41-78.
    • (1993) Ser. Number Theory , vol.1 , pp. 41-78
    • Fontaine, J.-M.1    Mazur, B.2
  • 13
    • 0001085970 scopus 로고
    • Free differential calculus. I: Derivation in the free group ring
    • [Fo]
    • [Fo] R. H. Fox, Free differential calculus. I: Derivation in the free group ring, Ann. Math. 57 (1953), 547-560.
    • (1953) Ann. Math. , vol.57 , pp. 547-560
    • Fox, R.H.1
  • 14
    • 0040755917 scopus 로고
    • Über die zentrale klassenzahl eines relativ-galoisschen zahlkörpers
    • [Fu]
    • [Fu] Y. Furuta, Über die Zentrale Klassenzahl eines relativ-galoisschen Zahlkörpers, J. Number Th. 3 (1971), 318-322.
    • (1971) J. Number Th. , vol.3 , pp. 318-322
    • Furuta, Y.1
  • 15
    • 0000684387 scopus 로고    scopus 로고
    • On the growth of p-class groups in p-class field towers
    • [Ha]
    • [Ha] F. Hajir, On the growth of p-class groups in p-class field towers, J. Algebra 188 (1997), 256-271.
    • (1997) J. Algebra , vol.188 , pp. 256-271
    • Hajir, F.1
  • 18
    • 0041787184 scopus 로고
    • A note on central class fields
    • [Ho]
    • [Ho] M. Horie, A note on central class fields, Abh. Math. Sem. Univ. Hamburg 57 (1986), 119-125.
    • (1986) Abh. Math. Sem. Univ. Hamburg , vol.57 , pp. 119-125
    • Horie, M.1
  • 19
    • 0013207718 scopus 로고
    • 1\{0,1, ∞}
    • [Ih]
    • 1\{0,1, ∞}, Invent. Math. 86 (1986), 427-459.
    • (1986) Invent. Math. , vol.86 , pp. 427-459
    • Ihara, Y.1
  • 20
    • 0042744618 scopus 로고
    • On Galois groups of local fields
    • [Iw]
    • [Iw] K. Iwasawa, On Galois groups of local fields, Trans. Amer. Math. Soc. 80 (1955), 448-469.
    • (1955) Trans. Amer. Math. Soc. , vol.80 , pp. 448-469
    • Iwasawa, K.1
  • 21
    • 0000725348 scopus 로고
    • Iwasawa modules up to isomorphism, algebraic number theory
    • [J] Academic Press, Boston, MA
    • [J] U. Jannsen, Iwasawa modules up to isomorphism, Algebraic number theory, Adv. Stud. Pure Math. 17, Academic Press, Boston, MA (1989), 171-207.
    • (1989) Adv. Stud. Pure Math. , vol.17 , pp. 171-207
    • Jannsen, U.1
  • 22
    • 0042789348 scopus 로고    scopus 로고
    • [Ka1] E-mail to the author (November 3) and personal communication (at Univ. of Toronto, in January)
    • [Ka1] M. Kapranov, E-mail to the author (November 3, 2000) and personal communication (at Univ. of Toronto, in January, 2001).
    • (2000)
    • Kapranov, M.1
  • 23
    • 0043290355 scopus 로고
    • Analogies between the Langlands correspondence and topological quantum field theory, functional analysis on the eve of the 21st century, in honor of the eightieth birthday of I. M. Gelfand
    • [Ka2] edited by S. Gindikin, J. Lepowsky and R. L. Wilson, Birkhäuser, Boston-Basel-Berlin
    • [Ka2] M. Kapranov, Analogies between the Langlands correspondence and topological quantum field theory, Functional Analysis on the Eve of the 21st Century, In honor of the eightieth birthday of I. M. Gelfand (edited by S. Gindikin, J. Lepowsky and R. L. Wilson), Progr. Math. 131, Birkhäuser, Boston-Basel-Berlin (1995), 119-151.
    • (1995) Progr. Math. , vol.131 , pp. 119-151
    • Kapranov, M.1
  • 24
    • 0013482557 scopus 로고
    • l-erweiterungen mit vorgegebenen verzweigungsstellen
    • [K1]
    • [K1] H. Koch, l-Erweiterungen mit vorgegebenen Verzweigungsstellen, J. reine angew. Math. 219 (1965), 30-61.
    • (1965) J. Reine Angew. Math. , vol.219 , pp. 30-61
    • Koch, H.1
  • 25
    • 84979309332 scopus 로고
    • Zum satz von golod-schafarewitsch
    • [K2]
    • [K2] H. Koch, Zum Satz von Golod-Schafarewitsch, Math. Nachr. 42 (1969), 321-333.
    • (1969) Math. Nachr. , vol.42 , pp. 321-333
    • Koch, H.1
  • 28
    • 51249182542 scopus 로고
    • Nilpotent completions and the Lie rings associated to link groups
    • [Ko]
    • [Ko] S. Kojima, Nilpotent completions and the Lie rings associated to link groups, Comment. Math. Helv. 58 (1983), 115-134.
    • (1983) Comment. Math. Helv. , vol.58 , pp. 115-134
    • Kojima, S.1
  • 29
    • 0001212423 scopus 로고
    • Classification of Demuškin groups
    • [L1]
    • [L1] J. P. Labute, Classification of Demuškin groups, Can. J. Math. 19 (1967), 106-132.
    • (1967) Can. J. Math. , vol.19 , pp. 106-132
    • Labute, J.P.1
  • 30
    • 0043290366 scopus 로고
    • The Lie algebra associated to the lower central series of a link group and Murasugi's conjecture
    • [L2]
    • [L2] J. P. Labute, The Lie algebra associated to the lower central series of a link group and Murasugi's conjecture, Proc. Amer. Math. Soc. 109 (1990), 951-956.
    • (1990) Proc. Amer. Math. Soc. , vol.109 , pp. 951-956
    • Labute, J.P.1
  • 31
    • 0000058044 scopus 로고
    • Groupes analytiques p-adiques
    • [La]
    • [La] M. Lazard, Groupes analytiques p-adiques, Publ. Math. I.H.E.S. 26 (1965), 389-603.
    • (1965) Publ. Math. I.H.E.S. , vol.26 , pp. 389-603
    • Lazard, M.1
  • 32
    • 0001229027 scopus 로고
    • 2(ℂ)
    • [Lu]
    • 2(ℂ), Ann. Math. 118 (1983), 115-130.
    • (1983) Ann. Math. , vol.118 , pp. 115-130
    • Lubotzky, A.1
  • 35
    • 84972549651 scopus 로고
    • Completion of link modules
    • [Mas]
    • [Mas] W. S. Massey, Completion of link modules, Duke Math. J. 47 No. 2 (1980), 399-420.
    • (1980) Duke Math. J. , vol.47 , Issue.2 , pp. 399-420
    • Massey, W.S.1
  • 36
    • 84972548460 scopus 로고
    • On a conjecture of K. Murasugi
    • [MT]
    • [MT] W. S. Massey and L. Traldi, On a conjecture of K. Murasugi, Pacific J. Math. 124 no. 1 (1986), 193-213.
    • (1986) Pacific J. Math. , vol.124 , Issue.1 , pp. 193-213
    • Massey, W.S.1    Traldi, L.2
  • 37
    • 0009299854 scopus 로고
    • Note on étale cohomology of number fields
    • [Maz1]
    • [Maz1] B. Mazur, Note on étale cohomology of number fields, Ann. Sci. EC. Norm. Sup. 6 (1973), 521-552.
    • (1973) Ann. Sci. EC. Norm. Sup. , vol.6 , pp. 521-552
    • Mazur, B.1
  • 38
    • 0041787177 scopus 로고    scopus 로고
    • [Maz2] E-mail to the author (October 17, 2000) on his unpublished mimeographed note (circa 1965)
    • [Maz2] B. Mazur, E-mail to the author (October 17, 2000) on his unpublished mimeographed note (circa 1965).
    • Mazur, B.1
  • 39
    • 0043290358 scopus 로고    scopus 로고
    • The theme of p-adic variation
    • [Maz3] Amer. Math. Soc., Providence, RI
    • [Maz3] B. Mazur, The theme of p-adic variation, Mathematics: frontiers and perspectives, Amer. Math. Soc., Providence, RI (2000), 433-459.
    • (2000) Mathematics: Frontiers and Perspectives , pp. 433-459
    • Mazur, B.1
  • 40
    • 0034381052 scopus 로고    scopus 로고
    • From dynamics on surfaces to rational points on curves
    • [MC]
    • [MC] C. McMullen, From dynamics on surfaces to rational points on curves, Bull. Amer. Math. Soc. 37 No. 2 (2000), 119-140.
    • (2000) Bull. Amer. Math. Soc. , vol.37 , Issue.2 , pp. 119-140
    • McMullen, C.1
  • 41
    • 0001349313 scopus 로고
    • Link groups
    • [M1]
    • [M1] J. W. Milnor, Link groups, Ann. Math. 59 (1954), 177-195.
    • (1954) Ann. Math. , vol.59 , pp. 177-195
    • Milnor, J.W.1
  • 42
    • 0002333550 scopus 로고
    • Isotopy of links
    • [M2] edited by R. H. Fox, D. S. Spencer and W. Tucker, Princeton Univ. Press, Princeton
    • [M2] J. W. Milnor, Isotopy of links, in: Algebraic Geometry and Topology, A symposium in honour of S. Lefschetz (edited by R. H. Fox, D. S. Spencer and W. Tucker), Princeton Univ. Press, Princeton (1957), 280-306.
    • (1957) Algebraic Geometry and Topology, a Symposium in Honour of S. Lefschetz , pp. 280-306
    • Milnor, J.W.1
  • 43
    • 23044519290 scopus 로고    scopus 로고
    • On Milnor's link invariants attached to certain Galois groups over ℚ
    • [Mo1]
    • [Mo1] M. Morishita, On Milnor's link invariants attached to certain Galois groups over ℚ, Proc. Japan Acad. 76 No. 2 (2000), 18-21.
    • (2000) Proc. Japan Acad. , vol.76 , Issue.2 , pp. 18-21
    • Morishita, M.1
  • 44
    • 0043290359 scopus 로고    scopus 로고
    • Knots and primes, 3-manifolds and number fields, algebraic number theory and related topics (Japanese)
    • [Mo2] Kyoto, Dec.
    • [Mo2] M. Morishita, Knots and primes, 3-manifolds and number fields, Algebraic number theory and related topics (Japanese), (Kyoto 2000, Dec.), Sūrikaisekikenkyūsho (RIMS) Kōkyūroku 1200 (2001), 103-115.
    • (2000) Sūrikaisekikenkyūsho (RIMS) Kōkyūroku , vol.1200 , pp. 103-115
    • Morishita, M.1
  • 45
    • 23044528973 scopus 로고    scopus 로고
    • A theory of genera for cyclic coverings of links
    • [Mo3]
    • [Mo3] M. Morishita, A theory of genera for cyclic coverings of links, Proc. Japan Acad. 77 No. 7 (2001), 115-118.
    • (2001) Proc. Japan Acad. , vol.77 , Issue.7 , pp. 115-118
    • Morishita, M.1
  • 46
    • 0042789306 scopus 로고
    • On Milnor's invariant for links
    • [Mu1]
    • [Mu1] K. Murasugi, On Milnor's invariant for links, Trans. Amer. Math. Soc. 124 (1966), 94-110.
    • (1966) Trans. Amer. Math. Soc. , vol.124 , pp. 94-110
    • Murasugi, K.1
  • 47
    • 84968503451 scopus 로고
    • On Milnor's link invariant for links. II. The Chen group
    • [Mu2]
    • [Mu2] K. Murasugi, On Milnor's link invariant for links. II. The Chen group, Trans. Amer. Math. Soc. 148 (1970), 41-61.
    • (1970) Trans. Amer. Math. Soc. , vol.148 , pp. 41-61
    • Murasugi, K.1
  • 48
    • 0042789344 scopus 로고
    • Nilpotent coverings of links and Milnor's invariant, low-dimensional topology
    • [Mu3] Cambridge Univ. Press, Cambridge-New York
    • [Mu3] K. Murasugi, Nilpotent coverings of links and Milnor's invariant, Low-dimensional topology, London Math. Soc. Lecture Note Ser. 95, Cambridge Univ. Press, Cambridge-New York (1985), 106-142.
    • (1985) London Math. Soc. Lecture Note Ser. , vol.95 , pp. 106-142
    • Murasugi, K.1
  • 49
    • 0043290362 scopus 로고    scopus 로고
    • A study of braids
    • [MK] Kluwer Academic Publ., Dordrecht-Boston-London
    • [MK] K. Murasugi and B. Kurpita, A Study of Braids, Math. Appl. 483, Kluwer Academic Publ., Dordrecht-Boston-London 1999.
    • (1999) Math. Appl. , vol.483
    • Murasugi, K.1    Kurpita, B.2
  • 51
    • 0000612564 scopus 로고
    • Formations de classes et modules d'Iwasawa, number theory noordwijkerhout 1983
    • [N]
    • [N] T. Nguyen-Quartg-Do, Formations de classes et modules d'Iwasawa, Number theory Noordwijkerhout 1983, Springer Lect. Notes Math. 1068 (1984), 167-185.
    • (1984) Springer Lect. Notes Math. , vol.1068 , pp. 167-185
    • Nguyen-Quartg-Do, T.1
  • 52
    • 84972566427 scopus 로고
    • On the existence of unramified p-extensions
    • [No]
    • [No] A. Nomura, On the existence of unramified p-extensions, Osaka J. Math. 28 (1991), 55-62.
    • (1991) Osaka J. Math. , vol.28 , pp. 55-62
    • Nomura, A.1
  • 53
    • 0039052032 scopus 로고
    • Central and genus class fields and the Hasse norm theorem
    • [Ra]
    • [Ra] M. Razor, Central and genus class fields and the Hasse norm theorem, Compos. Math. 35 no. 3 (1977), 281-298.
    • (1977) Compos. Math. , vol.35 , Issue.3 , pp. 281-298
    • Razor, M.1
  • 54
    • 0002668311 scopus 로고
    • Arithmetischer beweis des satzes über die anzahl der durch 4 teilbaren invarianten der absoluten klassengruppe im quadratischen zahlkörper
    • [Re1]
    • [Re1] L. Rédei, Arithmetischer Beweis des Satzes über die Anzahl der durch 4 teilbaren Invarianten der absoluten Klassengruppe im quadratischen Zahlkörper, J. reine angew. Math. 171 (1934), 55-60.
    • (1934) J. Reine Angew. Math. , vol.171 , pp. 55-60
    • Rédei, L.1
  • 55
    • 0006939533 scopus 로고
    • Ein neues zahlentheoretisches symbol mit anwendungen auf die theorie der quadratischen zahlkörper, I
    • [Re2]
    • [Re2] L. Rédei, Ein neues zahlentheoretisches Symbol mit Anwendungen auf die Theorie der quadratischen Zahlkörper, I, J. reine angew. Math. 180 (1938), 1-43.
    • (1938) J. Reine Angew. Math. , vol.180 , pp. 1-43
    • Rédei, L.1
  • 56
  • 57
    • 0042789333 scopus 로고    scopus 로고
    • Embedded incompressible surfaces and homology of ramified coverings of three-manifolds
    • [R2]
    • [R2] A. Reznikov, Embedded incompressible surfaces and homology of ramified coverings of three-manifolds, Sel. Math. New Ser. 6 (2000), 1-39.
    • (2000) Sel. Math. New Ser. , vol.6 , pp. 1-39
    • Reznikov, A.1
  • 60
    • 0009193308 scopus 로고    scopus 로고
    • Three-manifold subgroup growth, homology of coverings and simplicial volume
    • [RM]
    • [RM] A. Reznikov and P. Moree, Three-manifold subgroup growth, homology of coverings and simplicial volume, Asian J. Math. 1 No. 4 (1997), 764-768.
    • (1997) Asian J. Math. , vol.1 , Issue.4 , pp. 764-768
    • Reznikov, A.1    Moree, P.2
  • 62
    • 0001263079 scopus 로고
    • Extensions with prescribed ramification points
    • [S2]
    • [S2] I. R. Šafarevič, Extensions with prescribed ramification points (Russian), Inst. Hautes Et. Sci. Publ. Math. 18 (1963), 71-95.
    • (1963) Inst. Hautes Et. Sci. Publ. Math. , vol.18 , pp. 71-95
    • Šafarevič, I.R.1
  • 63
    • 84966234264 scopus 로고
    • p-homology, and volumes of hyperbolic 3-manifolds
    • [SW]
    • p-homology, and volumes of hyperbolic 3-manifolds, Trans. Amer. Math. Soc. 331 (1992), 895-917.
    • (1992) Trans. Amer. Math. Soc. , vol.331 , pp. 895-917
    • Shalen, P.1    Wagreich, P.2
  • 64
    • 0042288279 scopus 로고
    • Milnor's invariants and the Massey products
    • [T1] English transl.
    • [T1] V. G. Turaev, Milnor's invariants and the Massey products, English transl. J. Soviet Math. 12 (1979), 128-137.
    • (1979) J. Soviet Math. , vol.12 , pp. 128-137
    • Turaev, V.G.1
  • 65
    • 0010205308 scopus 로고
    • Nilpotent homotopy types of closed 3-manifolds
    • [T2]
    • [T2] V. G. Turaev, Nilpotent homotopy types of closed 3-manifolds, Springer Lect. Notes Math. 1060 (1984), 355-366.
    • (1984) Springer Lect. Notes Math. , vol.1060 , pp. 355-366
    • Turaev, V.G.1
  • 66
    • 0043290361 scopus 로고
    • Entrelacements sur spec(ℤ)
    • [Wa]
    • [Wa] J.-L. Waldspurger, Entrelacements sur Spec(ℤ), Bull. Soc. Math. 100 (1976), 113-139.
    • (1976) Bull. Soc. Math. , vol.100 , pp. 113-139
    • Waldspurger, J.-L.1
  • 67
    • 0002889497 scopus 로고
    • Duality theorems for Γ-extensions of algebraic number fields
    • [Wi]
    • [Wi] K. Wingberg, Duality theorems for Γ-extensions of algebraic number fields, Compos. Math. 55 (1985), 333-381.
    • (1985) Compos. Math. , vol.55 , pp. 333-381
    • Wingberg, K.1


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