Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-24T14:15:19.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Triangulating and recognising PL homology manifolds

Published online by Cambridge University Press:  24 October 2008

R. Ayala ,
A. Quintero  and
W. J. R. Mitchell
R. Ayala
Affiliation:
Departamento de Geometría y Topología, Faculdad de Matemáticas, Tarfia, s/n 41012-Sevilla, Spain
A. Quintero
Affiliation:
Departamento de Geometría y Topología, Faculdad de Matemáticas, Tarfia, s/n 41012-Sevilla, Spain
W. J. R. Mitchell
Affiliation:
Magdalene College, Cambridge, CB3 OAG
Get access Rights & Permissions [Opens in a new window]

Abstract

An earlier recognition theorem of one of the authors is extended to the bounded case, and conditions yielding concordance of triangulations are established.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 3 , November 1988 , pp. 497 - 504
Copyright
Copyright © Cambridge Philosophical Society 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ayala, R. and Quintero, A.. Topological collars in homology manifolds. Comment. Math. Univ. Math. St. Paul (to appear).Google Scholar
[2]Cannon, J. W.. The recognition problem; what is a topological manifold? Bull. Amer. Math. Soc. 84 (1978), 832–866.CrossRefGoogle Scholar
[3]Cannon, J. W., Bryant, J. L. and Lacher, R. C.. The structure of generalized manifolds having nonmanifold set of trivial dimension. In Proceedings of Georgia Conferense 1978 (Academic Press, 1979) pp. 261–300.Google Scholar
[4]Daverman, R. J.. Decompositions of Manifolds (Academic Press, 1986).Google Scholar
[5]Galewski, D. E. and Stern, R. J.. Classification of simplicial triangulations of topological manifolds. Ann. of Math. (2) 111 (1980), 1–34.CrossRefGoogle Scholar
[6]Hudson, J. F. P.. Piecewise Linear Topology (Benjamin. 1969).Google Scholar
[7]Maunder, C. R. F.. Algebraic Topology (Van Nostrand, 1970).Google Scholar
[8]Maunder, C. R. F.. Surgery on homology manifolds. II: The surgery exact sequence and an application to fake tori. J. London Math. Soc. (2) 12 (1975), 169–175.Google Scholar
[9]Mazur, B.. A note on some contractible 4-manifolds. Ann. of Math. (2) 73 (1961), 221–228.CrossRefGoogle Scholar
[10]McMillan, D. R.. A criterion for cellularity in a manifold. Ann. of Math. (2) 79 (1964), 327–337.CrossRefGoogle Scholar
[11]Mitchell, W. J. R.. A characterisation of piecewise linear homology manifolds. Math. Proc. Cambridge Philos. Soc. 93 (1983), 271–274.CrossRefGoogle Scholar
[12]Quinn, F.. Ends of maps I. Ann. of Math. (2) 110 (1979), 275–331.CrossRefGoogle Scholar
[13]Quinn, F.. Resolutions of homology manifolds and the topological characterization of manifolds: corrigendum. Invent. Math. 85 (1986), 653CrossRefGoogle Scholar
[14]Siebenmann, L. C.. The obstruction to finding a boundary for an open manifold of dimension > 5. Ph.D. Thesis, Princeton University (1965).+5.+Ph.D.+Thesis,+Princeton+University+(1965).>Google Scholar