Isovariant mappings of degree 1 and the Gap Hypothesis

Schultz, Reinhard¹

¹Department of Mathematics, University of California at Riverside, Riverside CA 92521, USA

Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 739-762

Résumé

Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions—isovariant and equivariant—often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

Détail

DOI : 10.2140/agt.2006.6.739

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

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