Acyclic decompositions of manifolds

Robert Jay Daverman and John J. Walsh

Vol. 109 (1983), No. 2, 291–303

DOI: 10.2140/pjm.1983.109.291

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