메뉴 건너뛰기




Volumn , Issue 765, 2003, Pages

Connectivity properties of group actions on non-positively curved spaces

(2)  Bieri, Robert a   Geoghegan, Ross a  

a NONE

Author keywords

Bieri Neumann Strebel invariant; CAT(0) space; Controlled topology; Finiteness properties; Isometric action; Non positively curved

Indexed keywords


EID: 85088340482     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: 10.1090/memo/0765     Document Type: Article
Times cited : (29)

References (44)
  • 1
    • 84963057320 scopus 로고
    • Bieri-strebel valuations (of finite rank)
    • [Å 86]
    • [Å 86] H. Åberg, Bieri-Strebel valuations (of finite rank), Proc. London Math. Soc. (3) 52 (1986), 269-304.
    • (1986) Proc. London Math. Soc. (3) , vol.52 , pp. 269-304
    • Åberg, H.1
  • 2
    • 0031534568 scopus 로고    scopus 로고
    • Morse theory and finiteness properties of groups
    • [BeBr 97]
    • [BeBr 97] M. Bestvina and N. Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997), 445-470.
    • (1997) Invent. Math. , vol.129 , pp. 445-470
    • Bestvina, M.1    Brady, N.2
  • 3
    • 0003772577 scopus 로고    scopus 로고
    • Homological dimension of discrete groups
    • [B 81] Queen Mary and Westfield College, London
    • [B 81] R. Bieri, Homological dimension of discrete groups, QMC Mathematics Notes, 2nc edition. Queen Mary and Westfield College, London.
    • QMC Mathematics Notes, 2nd Edition
    • Bieri, R.1
  • 4
    • 0013005992 scopus 로고    scopus 로고
    • Finiteness length and connectivity length for groups
    • [B 98] de Gruyter, Berlin
    • [B 98] R. Bieri, Finiteness length and connectivity length for groups, Geometric group theory down under (Canberra, 1996), 9-22, de Gruyter, Berlin, 1999.
    • (1999) Geometric Group Theory Down Under (Canberra, 1996) , pp. 9-22
    • Bieri, R.1
  • 6
    • 0012952950 scopus 로고    scopus 로고
    • Kernels of actions on non-positively curved spaces, Geometry and cohomology in group theory
    • [BG 98] (P.H. Kropholler, G. Niblo and R. Stöhr, ed.) Cambridge University Press, Cambridge
    • [BG 98] R. Bieri and R. Geoghegan, Kernels of actions on non-positively curved spaces, Geometry and cohomology in group theory (P.H. Kropholler, G. Niblo and R. Stöhr, ed.) London Math. Soc. Lecture Notes 252, Cambridge University Press, Cambridge, 1998, 24-38.
    • (1998) London Math. Soc. Lecture Notes , vol.252 , pp. 24-38
    • Bieri, R.1    Geoghegan, R.2
  • 7
    • 84961487768 scopus 로고
    • The geometry of the set of characters induced by valuations
    • [BGr 84]
    • [BGr 84] R. Bieri and J.R.J. Groves, The geometry of the set of characters induced by valuations, J. reine und angew. Math. 347 (1984), 168-195.
    • (1984) J. Reine und Angew. Math. , vol.347 , pp. 168-195
    • Bieri, R.1    Groves, J.R.J.2
  • 8
    • 0001271840 scopus 로고
    • A geometric invariant of discrete groups
    • [BNS 87]
    • [BNS 87] R. Bieri, W. Neumann and R. Strebel, A geometric invariant of discrete groups, Invent. Math. 90 (1987), 451-477.
    • (1987) Invent. Math. , vol.90 , pp. 451-477
    • Bieri, R.1    Neumann, W.2    Strebel, R.3
  • 9
    • 51249177208 scopus 로고
    • Valuations on free resolutions and higher geometric invariants of groups
    • [BRe 88]
    • [BRe 88] R. Bieri and B. Renz, Valuations on free resolutions and higher geometric invariants of groups, Comment Math. Helvetici 63 (1988), 464-497.
    • (1988) Comment Math. Helvetici , vol.63 , pp. 464-497
    • Bieri, R.1    Renz, B.2
  • 10
    • 51249185913 scopus 로고
    • Almost finitely presented soluble groups
    • [BS 78]
    • [BS 78] R. Bieri and R. Strebel, Almost finitely presented soluble groups, Comment. Math. Helv. 53 (1978), 258-278.
    • (1978) Comment. Math. Helv. , vol.53 , pp. 258-278
    • Bieri, R.1    Strebel, R.2
  • 11
    • 0000347445 scopus 로고
    • Valuations and finitely presented metabelian groups
    • [BS 80]
    • [BS 80] R. Bieri and R. Strebel, Valuations and finitely presented metabelian groups, Proc. London Math. Soc. (3) 41 (1980), 439-464.
    • (1980) Proc. London Math. Soc. (3) , vol.41 , pp. 439-464
    • Bieri, R.1    Strebel, R.2
  • 12
    • 0000398265 scopus 로고
    • A geometric invariant for modules over an Abelian group
    • [BS 81]
    • [BS 81] R. Bieri and R. Strebel, A geometric invariant for modules over an Abelian group, J. Reine und angew. Math. 322 (1981), 170-189.
    • (1981) J. Reine und Angew. Math. , vol.322 , pp. 170-189
    • Bieri, R.1    Strebel, R.2
  • 15
    • 0001964690 scopus 로고
    • Finiteness properties of groups
    • I]
    • I] K.S. Brown, Finiteness properties of groups, J. Pure and Applied Algebra 44 (1987), 45-75.
    • (1987) J. Pure and Applied Algebra , vol.44 , pp. 45-75
    • Brown, K.S.1
  • 16
    • 0000949256 scopus 로고
    • Trees, valuations and the Bieri-Neumann-Strebel invariant
    • II]
    • II] K.S. Brown, Trees, valuations and the Bieri-Neumann-Strebel invariant, Invent. Math. 90 (1987), 479-504.
    • (1987) Invent. Math. , vol.90 , pp. 479-504
    • Brown, K.S.1
  • 17
    • 0001306383 scopus 로고    scopus 로고
    • Finiteness properties of certain metabelian arithmetic groups in the function field case
    • [Bu]
    • [Bu] K.-U. Bux, Finiteness properties of certain metabelian arithmetic groups in the function field case, Proc. London Math. Soc. (3) 75 (1997), 308-322.
    • (1997) Proc. London Math. Soc. (3) , vol.75 , pp. 308-322
    • Bux, K.-U.1
  • 18
    • 0013005994 scopus 로고    scopus 로고
    • The Bestvina-Brady construction revisited: Geometric computation of the ∑-invariants for right angled Artin groups
    • [BuGo 99]
    • [BuGo 99] K.-U. Bux and C. Gonzalez, The Bestvina-Brady construction revisited: geometric computation of the ∑-invariants for right angled Artin groups, J. London Math. Soc. (2) 60 1999, 793-801.
    • (1999) J. London Math. Soc. (2) , vol.60 , pp. 793-801
    • Bux, K.-U.1    Gonzalez, C.2
  • 19
    • 0003535772 scopus 로고
    • [Du] Allyn and Bacon, Boston
    • [Du] J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.
    • (1966) Topology
    • Dugundji, J.1
  • 20
    • 0013002315 scopus 로고    scopus 로고
    • Pibered representations, an open condition
    • [Fa 99]
    • [Fa 99] F.T. Farrell, Pibered representations, an open condition, Topology and its Applications 96 (1999), 185-190.
    • (1999) Topology and Its Applications , vol.96 , pp. 185-190
    • Farrell, F.T.1
  • 21
    • 0013014829 scopus 로고
    • Epsilon surgery theory
    • [FePe 95] Proceedings 1993 Oberwolfach conference on Novikov conjectures, rigidity and index theorems, vol. 2, (A. Ranicki, ed.) Cambridge University Press
    • [FePe 95] S. Ferry and E.K. Pedersen, Epsilon surgery theory, Proceedings 1993 Oberwolfach conference on Novikov conjectures, rigidity and index theorems, vol. 2, (A. Ranicki, ed.) London Math. Soc. Lecture Notes, vol. 227, Cambridge University Press (1995), 167-226.
    • (1995) London Math. Soc. Lecture Notes , vol.227 , pp. 167-226
    • Ferry, S.1    Pedersen, E.K.2
  • 22
    • 0012961305 scopus 로고
    • Realizing group automorphisms
    • [FrLe 85]
    • [FrLe 85] D. Fried and R. Lee, Realizing group automorphisms, Contemp. Math. 36 (1985), 427-433.
    • (1985) Contemp. Math. , vol.36 , pp. 427-433
    • Fried, D.1    Lee, R.2
  • 25
    • 21744458191 scopus 로고    scopus 로고
    • The boundary of a Busemann space
    • [Ho 97]
    • [Ho 97] P.K. Hotchkiss, The boundary of a Busemann space, Proc. Amer. Math. Soc. 125 (1997) 1903-1912.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , pp. 1903-1912
    • Hotchkiss, P.K.1
  • 27
    • 0030587332 scopus 로고    scopus 로고
    • m-conjecture for a class of metabelian groups
    • [Ko 96]
    • m-conjecture for a class of metabelian groups, J. of Algebra 184 (1996), 1175-1204.
    • (1996) J. of Algebra , vol.184 , pp. 1175-1204
    • Kochloukova, D.1
  • 28
    • 0002363728 scopus 로고    scopus 로고
    • Higher generation subgroup sets and the ∑-invariants of graph groups
    • [MMV 98]
    • [MMV 98] J. Meier, H. Meinert, and L. VanWyk, Higher generation subgroup sets and the ∑-invariants of graph groups, Comment. Math. Helv. 73 (1998), 22-44.
    • (1998) Comment. Math. Helv. , vol.73 , pp. 22-44
    • Meier, J.1    Meinert, H.2    VanWyk, L.3
  • 29
    • 51249168010 scopus 로고
    • The geometric invariants of direct products of virtually free groups
    • [Me 94]
    • [Me 94] H. Meinert, The geometric invariants of direct products of virtually free groups, Comment. Math. Helvetici 69 (1994), 39-48.
    • (1994) Comment. Math. Helvetici , vol.69 , pp. 39-48
    • Meinert, H.1
  • 30
    • 0001425828 scopus 로고
    • The Bieri-Neumann-Strebel invariant for graph products of groups
    • [Me 95]
    • [Me 95] H. Meinert, The Bieri-Neumann-Strebel invariant for graph products of groups, J. Pure Appl. Algebra 103 (1995), 205-210.
    • (1995) J. Pure Appl. Algebra , vol.103 , pp. 205-210
    • Meinert, H.1
  • 33
    • 0012912186 scopus 로고
    • Normal subgroups with infinite cyclic quotient
    • [Ne 79]
    • [Ne 79] W.D. Neumann, Normal subgroups with infinite cyclic quotient, Math. Sci. 4 (1979), 143-148.
    • (1979) Math. Sci. , vol.4 , pp. 143-148
    • Neumann, W.D.1
  • 35
    • 0003282023 scopus 로고
    • Discrete subgroups of Lie groups
    • [Ra] Spring, Berlin
    • [Ra] M.S. Ragunathan, Discrete subgroups of Lie groups, Ergebnisse der Math., vol. 68, Spring, Berlin, 1972.
    • (1972) Ergebnisse der Math. , vol.68
    • Ragunathan, M.S.1
  • 37
    • 0013007165 scopus 로고
    • Geometric invariants and HNN-extensions
    • [Re 89] de Gruyter Verlag, Berlin
    • [Re 89] B. Renz, Geometric invariants and HNN-extensions, Group Theory (Singapore 1987), de Gruyter Verlag, Berlin 1989, 465-484.
    • (1989) Group Theory (Singapore 1987) , pp. 465-484
    • Renz, B.1
  • 38
    • 0000354326 scopus 로고
    • Topological methods in group theory, homological group theory
    • [SW 79] (C.T.C. Wall, ed.) Cambridge University Press, Cambridge
    • [SW 79] G.P. Scott and C.T.C. Wall, Topological methods in group theory, Homological group theory (C.T.C. Wall, ed.) London Math. Soc. Lecture Notes 36, Cambridge University Press, Cambridge, 1979, 137-203.
    • (1979) London Math. Soc. Lecture Notes , vol.36 , pp. 137-203
    • Scott, G.P.1    Wall, C.T.C.2
  • 39
    • 0004211763 scopus 로고
    • [Se] Springer, Berlin
    • [Se] J.-P. Serre. Trees, Springer, Berlin, 1980.
    • (1980) Trees
    • Serre, J.-P.1
  • 40
    • 84968505445 scopus 로고
    • A Vietoris mapping theorem for homotopy
    • [Sm 57]
    • [Sm 57] S. Smale, A Vietoris mapping theorem for homotopy, Proc. Amer. Math. Soc. 8 (1957), 604-610.
    • (1957) Proc. Amer. Math. Soc. , vol.8 , pp. 604-610
    • Smale, S.1
  • 41
    • 0032571056 scopus 로고    scopus 로고
    • Approximate finiteness properties of infinite groups
    • [Sta 98]
    • [Sta 98] C. Stark, Approximate finiteness properties of infinite groups, Topology 37 (1998) 1073-1088.
    • (1998) Topology , vol.37 , pp. 1073-1088
    • Stark, C.1
  • 42
    • 0000989069 scopus 로고
    • Homological properties of certain arithmetic groups in the function field case
    • [St 80]
    • [St 80] U. Stuhler, Homological properties of certain arithmetic groups in the function field case, Invent. Math. 57 (1980), 263-281.
    • (1980) Invent. Math. , vol.57 , pp. 263-281
    • Stuhler, U.1
  • 43
    • 0000324511 scopus 로고
    • On discrete subgroups of Lie groups
    • [We 60]
    • [We 60] A. Weil, On discrete subgroups of Lie groups, Ann. Math. 72 (1960), 369-384.
    • (1960) Ann. Math. , vol.72 , pp. 369-384
    • Weil, A.1
  • 44
    • 0000522511 scopus 로고
    • Remarks on the cohomology of groups
    • [We 64]
    • [We 64] A. Weil, Remarks on the cohomology of groups, Ann. Math. 80 (1964), 149-157.
    • (1964) Ann. Math. , vol.80 , pp. 149-157
    • Weil, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.