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2006 Isovariant mappings of degree 1 and the Gap Hypothesis
Reinhard Schultz
Algebr. Geom. Topol. 6(2): 739-762 (2006). DOI: 10.2140/agt.2006.6.739

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Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions—isovariant and equivariant—often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

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Reinhard Schultz. "Isovariant mappings of degree 1 and the Gap Hypothesis." Algebr. Geom. Topol. 6 (2) 739 - 762, 2006. https://doi.org/10.2140/agt.2006.6.739

Information

Received: 29 September 2005; Revised: 8 May 2006; Accepted: 12 May 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1173.55300
MathSciNet: MR2240914
Digital Object Identifier: 10.2140/agt.2006.6.739

Subjects:
Primary: 55P91 , 57S17
Secondary: 55R91 , 55S15 , 55S91

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

Rights: Copyright © 2006 Mathematical Sciences Publishers

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