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Volumn 358, Issue 12, 2006, Pages 5257-5270

The 3-manifold recognition problem

Author keywords

Generalized 3 manifold; Locally 1 coconnected; Relative simplicial approximation; Resolvable; Simplicial approximation property; Tame embedding

Indexed keywords


EID: 33845795769     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-05-03786-4     Document Type: Article
Times cited : (5)

References (24)
  • 1
    • 84884522495 scopus 로고
    • An alternative proof of M. Brown's theorem on inverse sequences of near homeomorphisms
    • (Dubrovnik), Lecture Notes in Math., Springer, Berlin, New York. MR89d:54003
    • F. D. Ancel, An alternative proof of M. Brown's theorem on inverse sequences of near homeomorphisms, Geometric topology and shape theory (Dubrovnik, 1986), pp. 1-2, Lecture Notes in Math., vol. 1283, Springer, Berlin, New York, 1987. MR89d:54003
    • (1986) Geometric Topology and Shape Theory , vol.1283 , pp. 1-2
    • Ancel, F.D.1
  • 2
    • 0003273669 scopus 로고
    • Cellular decompositions of 3-manifolds that yield 3-manifolds
    • Amer. Math. Soc., Providence, RI. MR54:1225
    • Steve Armentrout, Cellular decompositions of 3-manifolds that yield 3-manifolds, Memoirs Amer. Math. Soc., No. 107, Amer. Math. Soc., Providence, RI, 1971. MR54:1225
    • (1971) Memoirs Amer. Math. Soc. , vol.107
    • Armentrout, S.1
  • 4
    • 0011512828 scopus 로고
    • A surface is tame if its complement is 1-ULC
    • MR24:A1117
    • R. H. Bing, A surface is tame if its complement is 1-ULC, Trans. Amer. Math. Soc. 101 (1961), 294-305. MR24:A1117
    • (1961) Trans. Amer. Math. Soc. , vol.101 , pp. 294-305
    • Bing, R.H.1
  • 5
    • 0003384875 scopus 로고
    • Generalized manifolds, revisited
    • (Proc. Inst., Univ. of Georgia, Athens, Ga, 1969), Markham, Chicago, Ill. MR43:1193
    • G. E. Bredon, Generalized manifolds, revisited, 1970 Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga, 1969), pp. 461-469, Markham, Chicago, Ill., 1970. MR43:1193
    • (1970) 1970 Topology of Manifolds , pp. 461-469
    • Bredon, G.E.1
  • 6
    • 84968466639 scopus 로고
    • Some applications of an approximation theorem for inverse limits
    • MR22:5959
    • Morton Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478-483. MR22:5959
    • (1960) Proc. Amer. Math. Soc. , vol.11 , pp. 478-483
    • Brown, M.1
  • 7
    • 0030534879 scopus 로고    scopus 로고
    • Topology of homology manifolds
    • MR97b:57017
    • J. Bryant, S. Ferry, W. Mio and S. Weinberger, Topology of homology manifolds, Ann. of Math. (2) 143 (1996), no. 3, 435-467. MR97b:57017
    • (1996) Ann. of Math. (2) , vol.143 , Issue.3 , pp. 435-467
    • Bryant, J.1    Ferry, S.2    Mio, W.3    Weinberger, S.4
  • 9
    • 0000550233 scopus 로고
    • The recognition problem: What is a topological manifold?
    • MR58:13043
    • J. W. Cannon, The recognition problem: what is a topological manifold? Bull. Amer. Math. Soc. 84 (1978), 832-866. MR58:13043
    • (1978) Bull. Amer. Math. Soc. , vol.84 , pp. 832-866
    • Cannon, J.W.1
  • 10
    • 84968482088 scopus 로고
    • A new proof for the Hosay-Lininger theorem about crumpled cubes
    • MR39:7578
    • R. J. Daverman, A new proof for the Hosay-Lininger theorem about crumpled cubes, Proc. Amer. Math. Soc. 23 (1969), 52-54. MR39:7578
    • (1969) Proc. Amer. Math. Soc. , vol.23 , pp. 52-54
    • Daverman, R.J.1
  • 11
    • 0003360611 scopus 로고
    • Decompositions of manifolds
    • Academic Press, Inc., Orlando, Fl. MR88a:57001
    • R. J. Daverman, Decompositions of Manifolds, Pure and Applied Mathematics, 124, Academic Press, Inc., Orlando, Fl., 1986. MR88a:57001
    • (1986) Pure and Applied Mathematics , vol.124
    • Daverman, R.J.1
  • 12
    • 0011474366 scopus 로고
    • General position properties that characterize 3-manifolds
    • MR93d:57038
    • R. J. Daverman and D. R. Repovš, General position properties that characterize 3-manifolds, Canad. J. Math. 44 (1992), 234-251. MR93d:57038
    • (1992) Canad. J. Math. , vol.44 , pp. 234-251
    • Daverman, R.J.1    Repovš, D.R.2
  • 14
    • 84968481768 scopus 로고
    • Some results on crumpled cubes
    • MR31:2717
    • L. L. Lininger, Some results on crumpled cubes, Trans. Amer. Math. Soc. 118 (1965), 534-549. MR31:2717
    • (1965) Trans. Amer. Math. Soc. , vol.118 , pp. 534-549
    • Lininger, L.L.1
  • 15
    • 84968468194 scopus 로고
    • A criterion for cellularity in a manifold
    • MR34:8392
    • D. R. McMillan, Jr., A criterion for cellularity in a manifold. II. Trans. Amer. Math. Soc. 126 (1967), 217-224. MR34:8392
    • (1967) II. Trans. Amer. Math. Soc. , vol.126 , pp. 217-224
    • McMillan Jr., D.R.1
  • 16
    • 84966217688 scopus 로고
    • Defining the boundary of a homology manifold
    • MR90m:57015
    • W. J. R. Mitchell, Defining the boundary of a homology manifold, Proc. Amer. Math. Soc. 110 (1990), 509-513. MR90m:57015
    • (1990) Proc. Amer. Math. Soc. , vol.110 , pp. 509-513
    • Mitchell, W.J.R.1
  • 18
    • 33845798069 scopus 로고
    • 1-FLG complexes are tame in 3-manifolds
    • MR47:5877
    • Victor A. Nicholson, 1-FLG complexes are tame in 3-manifolds, General Topology and Appl. 2 (1972), 277-285. MR47:5877
    • (1972) General Topology and Appl. , vol.2 , pp. 277-285
    • Nicholson, V.A.1
  • 19
    • 0001667031 scopus 로고
    • An obstruction to the resolution of homology manifolds
    • MR88j:57016
    • Frank Quinn, An obstruction to the resolution of homology manifolds, Michigan Math. J. 34 (1987), 285-291. MR88j:57016
    • (1987) Michigan Math. J. , vol.34 , pp. 285-291
    • Quinn, F.1
  • 20
    • 0001827897 scopus 로고
    • Separation and union theorems for generalized manifolds with boundary
    • MR22:11388
    • Frank Raymond, Separation and union theorems for generalized manifolds with boundary, Michigan Math. J. 7 (1960), 7-21. MR22:11388
    • (1960) Michigan Math. J. , vol.7 , pp. 7-21
    • Raymond, F.1
  • 21
    • 0001575814 scopus 로고
    • Approximating cellular maps by homeomorphisms
    • MR45:4431
    • L. C. Siebenmann, Approximating cellular maps by homeomorphisms, Topology 11 (1972), 271-294. MR45:4431
    • (1972) Topology , vol.11 , pp. 271-294
    • Siebenmann, L.C.1
  • 22
    • 0842337896 scopus 로고
    • An extension of the Loop theorem and resolutions of generalized 3-manifolds with 0-dimensional singular set
    • MR86f:57007
    • T. L. Thickstun, An extension of the Loop theorem and resolutions of generalized 3-manifolds with 0-dimensional singular set, Invent. Math. 78 (1984), 161-222. MR86f:57007
    • (1984) Invent. Math. , vol.78 , pp. 161-222
    • Thickstun, T.L.1
  • 23
    • 0842303678 scopus 로고    scopus 로고
    • Resolutions of generalized 3-manifolds whose singular sets have general position dimension one
    • MR2005b:57043
    • T. L. Thickstun, Resolutions of generalized 3-manifolds whose singular sets have general position dimension one, Topology Appl. 138 (2004), 61-95. MR2005b:57043
    • (2004) Topology Appl. , vol.138 , pp. 61-95
    • Thickstun, T.L.1
  • 24
    • 33845754989 scopus 로고
    • Amer. Math. Soc. Colloquium Publ., Amer. Math. Soc., Providence, RI. MR82a:57001
    • R. L. Wilder, Topology of manifolds. Amer. Math. Soc. Colloquium Publ., vol. 32, Amer. Math. Soc., Providence, RI, 1979. MR82a:57001
    • (1979) Topology of Manifolds , vol.32
    • Wilder, R.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.