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Peripheral acyclicity in 3-manifolds

Part of: Topological manifolds PL-topology

Published online by Cambridge University Press:  09 April 2009

Dušan Repovš
Dušan Repovš
Affiliation:
Department of MathematicsUniversity of TexasAustin, Texas 78712, U. S. A.
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Abstract

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We study weak and strong peripheral 1-acyclicity, a homology version of D. R. McMillan, Jr.'s weak cellularity criterion and cellularity criterion, for embeddings of compacta in 3-manifolds. In contrast with the two cellularity criteria we prove that the two peripheral acyclicities are equivalent and moreover, for compacta of dimension at most 1, independent of the embedding. We also give some results concerning regular neighborhoods of compact polyhedra in 3-manifolds.

MSC classification

Secondary: 57N60: Cellularity 57N40: Neighborhoods of submanifolds 57Q40: Regular neighborhoods
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 3 , June 1987 , pp. 312 - 321
Copyright
Copyright © Australian Mathematical Society 1987

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