메뉴 건너뛰기




Volumn 6, Issue 3, 1996, Pages 245-270

4-dimensional Busemann G-spaces are 4-manifolds

Author keywords

Cell like resolution; Geodesic space; Homology manifold; Sythentic geometry

Indexed keywords


EID: 0030240120     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/0926-2245(96)82421-1     Document Type: Article
Times cited : (7)

References (63)
  • 4
    • 0011515951 scopus 로고
    • A three-dimensional spheroidal space which is not a sphere
    • [4] S. Armentrout, A three-dimensional spheroidal space which is not a sphere, Fund. Math. 68 (1970) 183-186.
    • (1970) Fund. Math. , vol.68 , pp. 183-186
    • Armentrout, S.1
  • 5
    • 0003273669 scopus 로고
    • Cellular decompositions of 3-manifolds that yield 3-manifolds
    • [5] S. Armentrout, Cellular decompositions of 3-manifolds that yield 3-manifolds, Mem. Am. Math. Soc. 107 (1971).
    • (1971) Mem. Am. Math. Soc. , vol.107
    • Armentrout, S.1
  • 6
    • 27544450480 scopus 로고
    • The finite dimensionality problem for Busemann's G-spaces
    • [6] V. Berestovsky, The finite dimensionality problem for Busemann's G-spaces, Siberian J. Math. 18 (1977) 219-221.
    • (1977) Siberian J. Math. , vol.18 , pp. 219-221
    • Berestovsky, V.1
  • 7
    • 0011512828 scopus 로고
    • A surface is tame if its complement is 1-ULC
    • [7] R.H. Bing, A surface is tame if its complement is 1-ULC, Trans. Am. Math. Soc. 101 (1961) 294-305.
    • (1961) Trans. Am. Math. Soc. , vol.101 , pp. 294-305
    • Bing, R.H.1
  • 8
    • 0003384875 scopus 로고
    • Generalized manifolds revisited
    • J.C. Cantrell and C.H. Edwards, eds., Proceeding of the University of Georgia Topology of Manifolds Institute Markham, Chicago
    • [8] G. Bredon, Generalized manifolds revisited, in: J.C. Cantrell and C.H. Edwards, eds., Topology of Manifolds, Proceeding of the University of Georgia Topology of Manifolds Institute (Markham, Chicago, 1970) 461-469
    • (1970) Topology of Manifolds , pp. 461-469
    • Bredon, G.1
  • 9
    • 84968475663 scopus 로고
    • The monotone union of open cells is an open cell
    • [9] M. Brown, The monotone union of open cells is an open cell, Proc. Am. Math. Soc. 12 (1961) 812-814.
    • (1961) Proc. Am. Math. Soc. , vol.12 , pp. 812-814
    • Brown, M.1
  • 10
    • 84879168733 scopus 로고
    • A proof of the generalized Schoenflies theorem
    • [10] M. Brown, A proof of the generalized Schoenflies theorem, Bull. Am. Math. Soc. 66 (1960) 74-76.
    • (1960) Bull. Am. Math. Soc. , vol.66 , pp. 74-76
    • Brown, M.1
  • 11
    • 0011518711 scopus 로고
    • Homogeneous ENR's
    • [11] J. Bryant, Homogeneous ENR's, Top. and its Appl. 27 (1987) 301-306.
    • (1987) Top. and Its Appl. , vol.27 , pp. 301-306
    • Bryant, J.1
  • 14
    • 33646864986 scopus 로고
    • Aleksandrov's spaces with curvature bounded from below, I
    • [14] Y. Burago, M. Gromov and G. Perlman, Aleksandrov's spaces with curvature bounded from below, I, Russian Math. Surveys 47 (1992) (2) 1-58.
    • (1992) Russian Math. Surveys , vol.47 , Issue.2 , pp. 1-58
    • Burago, Y.1    Gromov, M.2    Perlman, G.3
  • 16
    • 0003284254 scopus 로고
    • Metric methods in Finsler spaces and in the foundations of geometry
    • Princeton University Press, Princeton
    • [16] H. Busemann, Metric Methods in Finsler Spaces and in the Foundations of Geometry, Ann. Math. Study 8 (Princeton University Press, Princeton, 1942).
    • (1942) Ann. Math. Study , vol.8
    • Busemann, H.1
  • 17
    • 0011412339 scopus 로고
    • On spaces in which two points determine a geodesic
    • [17] H. Busemann, On spaces in which two points determine a geodesic, Trans. Am. Math. Soc. 54 (1943) 171-184.
    • (1943) Trans. Am. Math. Soc. , vol.54 , pp. 171-184
    • Busemann, H.1
  • 20
    • 38249000169 scopus 로고
    • Novel results in the geometry of geodesics
    • [20] H. Busemann and B.B. Phadke, Novel results in the geometry of geodesics, Advances in Math. 101 (1993) 180-219.
    • (1993) Advances in Math. , vol.101 , pp. 180-219
    • Busemann, H.1    Phadke, B.B.2
  • 21
    • 0011417453 scopus 로고
    • Taming cell-like embedding relations
    • L.C. Glaser and T.B. Rushing, eds., Lecture Notes in Math. Springer-Verlag, Berlin and New York
    • [21] J.W. Cannon, Taming cell-like embedding relations, in: L.C. Glaser and T.B. Rushing, eds., Geometric Topology, Lecture Notes in Math. 438 (Springer-Verlag, Berlin and New York, 1975) 66-118.
    • (1975) Geometric Topology , vol.438 , pp. 66-118
    • Cannon, J.W.1
  • 24
    • 0011510696 scopus 로고
    • Decompositions of manifolds into codimension one submanifolds
    • [24] R.J. Daverman, Decompositions of manifolds into codimension one submanifolds, Compositio Math. 55 (1985) 185-207.
    • (1985) Compositio Math. , vol.55 , pp. 185-207
    • Daverman, R.J.1
  • 25
    • 84972529889 scopus 로고
    • Detecting the disjoint disks property
    • [25] R.J. Daverman, Detecting the disjoint disks property, Pacific J. Math. 93 (1981) 277-298.
    • (1981) Pacific J. Math. , vol.93 , pp. 277-298
    • Daverman, R.J.1
  • 26
    • 0011474366 scopus 로고
    • General position properties that characterize 3-manifolds
    • [26] R.J. Daverman and D. Repovš, General position properties that characterize 3-manifolds, Can. J. Math. 44 (1992) 234-251.
    • (1992) Can. J. Math. , vol.44 , pp. 234-251
    • Daverman, R.J.1    Repovš, D.2
  • 29
    • 0011412340 scopus 로고
    • Sheaves that are locally constant with applications to homology manifolds
    • S. Mardešić and J. Segal, eds., Lecture Notes in Math. Springer-Verlag, Berlin and New York
    • [29] J. Dydak and J.J. Walsh, Sheaves that are locally constant with applications to homology manifolds, in: S. Mardešić and J. Segal, eds., Geometric Topology and Shape Theory, Lecture Notes in Math. 1283 (Springer-Verlag, Berlin and New York, 1987) 65-87.
    • (1987) Geometric Topology and Shape Theory , vol.1283 , pp. 65-87
    • Dydak, J.1    Walsh, J.J.2
  • 30
    • 0001301320 scopus 로고
    • Homotoping ε-maps to homeomorphisms
    • [30] S.C. Ferry, Homotoping ε-maps to homeomorphisms, Amer. J. Math. 101 (1979) 567-582.
    • (1979) Amer. J. Math. , vol.101 , pp. 567-582
    • Ferry, S.C.1
  • 33
    • 84972496726 scopus 로고
    • The topology of 4-manifolds
    • [33] M.H. Freedman, The topology of 4-manifolds, J. Diff. Geom. 17 (1982) 357-454.
    • (1982) J. Diff. Geom. , vol.17 , pp. 357-454
    • Freedman, M.H.1
  • 36
    • 0000976022 scopus 로고
    • Geometric finiteness theorems via controlled topology
    • [36] K. Grove, P. Petersen and H. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990) 205-213; correction: Invent. Math. 104 (1991) 221-222.
    • (1990) Invent. Math. , vol.99 , pp. 205-213
    • Grove, K.1    Petersen, P.2    Wu, H.3
  • 37
    • 0010717327 scopus 로고
    • [36] K. Grove, P. Petersen and H. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990) 205-213; correction: Invent. Math. 104 (1991) 221-222.
    • (1991) Invent. Math. , vol.104 , pp. 221-222
  • 40
    • 0004220560 scopus 로고
    • Springer-Verlag, Berlin-Heidelberg-New York
    • [39] T.W. Hungerford, Algebra (Springer-Verlag, Berlin-Heidelberg-New York, 1984).
    • (1984) Algebra
    • Hungerford, T.W.1
  • 41
    • 0011481729 scopus 로고
    • Any 3-dimensional G-space is a manifold
    • [40] B. Krakus, Any 3-dimensional G-space is a manifold, Bull. Acad. Pol. Sci. 16 (1968) 737-740.
    • (1968) Bull. Acad. Pol. Sci. , vol.16 , pp. 737-740
    • Krakus, B.1
  • 42
    • 0011518715 scopus 로고
    • Sur les espaces localement connexes et pé aniens en dimension n
    • [41] K. Kuratowski, Sur les espaces localement connexes et pé aniens en dimension n, Fund. Math. 25 (1935) 269-287.
    • (1935) Fund. Math. , vol.25 , pp. 269-287
    • Kuratowski, K.1
  • 45
    • 0011458841 scopus 로고
    • A criterion for cellularity in a manifold
    • [44] D.R. McMillan, Jr., A criterion for cellularity in a manifold, Ann. of Math. 79 (1964) 327-337.
    • (1964) Ann. of Math. , vol.79 , pp. 327-337
    • McMillan D.R., Jr.1
  • 46
    • 84966217688 scopus 로고
    • Defining the boundary of a homology manifold
    • [45] W.J.R. Mitchell, Defining the boundary of a homology manifold, Proc. Am. Math. Soc. 110 (1990) 509-513.
    • (1990) Proc. Am. Math. Soc. , vol.110 , pp. 509-513
    • Mitchell, W.J.R.1
  • 47
    • 0011506127 scopus 로고
    • The topology of cell-like mappings
    • Cala Gonone (Sardinia)
    • [46] W.J.R. Mitchell and D. Repovš, The topology of cell-like mappings, Proc. Conf. Diff. Geom. and Top., Cala Gonone (Sardinia) 63 (1988) 265-300.
    • (1988) Proc. Conf. Diff. Geom. and Top. , vol.63 , pp. 265-300
    • Mitchell, W.J.R.1    Repovš, D.2
  • 48
    • 0011510698 scopus 로고
    • Locally homogeneous spaces
    • [47] D. Montgomery, Locally homogeneous spaces, Ann. of Math. 51 (1950) 261-271.
    • (1950) Ann. of Math. , vol.51 , pp. 261-271
    • Montgomery, D.1
  • 49
    • 0000427353 scopus 로고
    • Concerning upper semicontinous collections of continua
    • [48] R.L. Moore, Concerning upper semicontinous collections of continua, Trans. Am. Math. Soc. 27 (1925) 416-428.
    • (1925) Trans. Am. Math. Soc. , vol.27 , pp. 416-428
    • Moore, R.L.1
  • 53
    • 84972517086 scopus 로고
    • Ends of maps III: Dimensions 4 and 5
    • [52] F. Quinn, Ends of maps III: Dimensions 4 and 5, J. Diff. Geo. 17 (1982) 503-521.
    • (1982) J. Diff. Geo. , vol.17 , pp. 503-521
    • Quinn, F.1
  • 54
    • 0001667031 scopus 로고
    • An obstruction to the resolution of homology manifolds
    • [53] F. Quinn, An obstruction to the resolution of homology manifolds, Mich. Math. J. 34 (1987) 285-291.
    • (1987) Mich. Math. J. , vol.34 , pp. 285-291
    • Quinn, F.1
  • 55
    • 0001827897 scopus 로고
    • Separation and union theorems for generalized manifolds with boundary
    • [54] F. Raymond, Separation and union theorems for generalized manifolds with boundary, Mich. Math. J. 7 (1960) 7-21.
    • (1960) Mich. Math. J. , vol.7 , pp. 7-21
    • Raymond, F.1
  • 56
    • 0000721625 scopus 로고
    • Monotone transformations of 2-dimensional manifolds
    • [55] J.H. Roberts and N.E. Steenrod, Monotone transformations of 2-dimensional manifolds, Ann. of Math. 39 (1938) 851-862.
    • (1938) Ann. of Math. , vol.39 , pp. 851-862
    • Roberts, J.H.1    Steenrod, N.E.2
  • 57
    • 0001575814 scopus 로고
    • Approximating cellular maps by homeomorphisms
    • [56] L.C. Siebenmann, Approximating cellular maps by homeomorphisms, Topology 11 (1972) 271-294.
    • (1972) Topology , vol.11 , pp. 271-294
    • Siebenmann, L.C.1
  • 58
  • 61
    • 0001997483 scopus 로고
    • Mapping Hilbert cube manifolds to ANR's: A solution of a conjecture of Borsuk
    • [60] J.E. West, Mapping Hilbert cube manifolds to ANR's: a solution of a conjecture of Borsuk, Ann. of Math. 106 (1977) 1-18.
    • (1977) Ann. of Math. , vol.106 , pp. 1-18
    • West, J.E.1
  • 62
    • 0011502810 scopus 로고
    • A.M.S. Colloq. Publ. Am. Math. Soc., Providence
    • [61] R. Wilder, Topology of Manifolds, A.M.S. Colloq. Publ. 32 (Am. Math. Soc., Providence, 1963).
    • (1963) Topology of Manifolds , vol.32
    • Wilder, R.1
  • 63
    • 0011513196 scopus 로고
    • Some characterizations of generalized manifolds with boundaries
    • [62] P. White, Some characterizations of generalized manifolds with boundaries, Can. J. Math. 4 (1952) 329-342.
    • (1952) Can. J. Math. , vol.4 , pp. 329-342
    • White, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.