Volume 6, issue 2 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Isovariant mappings of degree 1 and the Gap Hypothesis

Reinhard Schultz

Algebraic & Geometric Topology 6 (2006) 739–762

arXiv: 0904.0599

Abstract

Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions—isovariant and equivariant—often coincide under a condition called the Gap Hypothesis; the proofs use deep results in geometric topology. This paper analyzes the difference between the two types of maps from a homotopy theoretic viewpoint more generally for degree one maps if the manifolds satisfy the Gap Hypothesis, and it gives a more homotopy theoretic proof of the Straus–Browder result.

Keywords
Blakers–Massey Theorem, deleted cyclic reduced product, diagram category, diagram cohomology, equivariant mapping, Gap Hypothesis, group action, homotopy equivalence, isovariant mapping, normally straightened mapping
Mathematical Subject Classification 2000
Primary: 55P91, 57S17
Secondary: 55R91, 55S15, 55S91
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Publication
Received: 29 September 2005
Revised: 8 May 2006
Accepted: 12 May 2006
Published: 12 June 2006
Authors
Reinhard Schultz
Department of Mathematics
University of California at Riverside
Riverside CA 92521
USA