Vol. 109, No. 2, 1983

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ISSN: 0030-8730
Acyclic decompositions of manifolds

Robert Jay Daverman and John J. Walsh

Vol. 109 (1983), No. 2, 291–303
Abstract

This paper develops techniques for generating decompositions of manifolds into homologically acyclic compacta. For n 3 it presents examples of decompositions of the n-sphere Sn that are totally acyclic, in the sense that each decomposition element is an acyclic but non-cell-like set. One class of examples yields non-ANR’s as quotient spaces; another class (for n > 3) yields ANR’s. The distinction essentially depends upon whether the decomposition elements are nearly 1-movable.

Mathematical Subject Classification 2000
Primary: 54B15
Secondary: 57P05
Milestones
Received: 21 April 1981
Published: 1 December 1983
Authors
Robert Jay Daverman
John J. Walsh