Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-18T03:03:56.292Z Has data issue: false hasContentIssue false
  • English
  • Français

On spines of 3-manifolds with boundary

Part of: Topological manifolds

Published online by Cambridge University Press:  09 April 2009

C. McA. Gordon
C. McA. Gordon
Affiliation:
Department of Mathematics, The University of Texas at Austin, Austin, TX 78712-1082, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a simple necessary and sufficient condition for the inclusion map of a subpolyhedron into a compact 3-manifold with non-empty boundary to be a homotopy equivalence.

MSC classification

Secondary: 57N10: Topology of general $3$-manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 1 , August 1993 , pp. 132 - 136
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Cohen, M. M., ‘Whitehead torsion, group extensions, and Zeeman's conjecture in high dimensions’, Topology 16 (1977), 79–88.CrossRefGoogle Scholar
[2]Dunwoody, M. J., ‘The homotopy type of a two-dimensional complex’, Bull. London Math. Soc. 8 (1976), 282–285.CrossRefGoogle Scholar
[3]Kong, T. Y., Litherland, R. and Rosenfeld, A., ‘Problems in the topology of binary images’, in: Open Problems in Topology (eds. van Mill, J. and Reed, G. M.) (North Holland, 1990).Google Scholar
[4]Metzler, W., ‘Über den Homotopietyp zweidimensionaler CW-Komplexe und Elementartransformationen bei Darstellungen von Gruppen durch Erzeugende und definierende Relationen’, J. reine angew. Math. 285 (1976), 7–23.Google Scholar