Isovariant mappings of degree 1 and the Gap Hypothesis

Schultz, Reinhard

doi:10.2140/agt.2006.6.739

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Isovariant mappings of degree 1 and the Gap Hypothesis

Reinhard Schultz

Algebraic & Geometric Topology 6 (2006) 739–762

DOI: 10.2140/agt.2006.6.739

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Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions—isovariant and equivariant—often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

Volume 6, issue 2 (2006)