Isovariant mappings of degree 1 and the Gap Hypothesis

Details Isovariant mappings of degree 1 and the Gap Hypothesis Isovariant mappings of degree 1 and the Gap Hypothesis

2009-04-03

arxiv.org/abs/0904.0599v1

Algebr. Geom. Topol. 6 (2006) 739-762

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 12 June 2006

Scientific paper

10.2140/agt.2006.6.739

Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions - isovariant and equivariant - often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