Algebraic & Geometric Topology

Isovariant mappings of degree 1 and the Gap Hypothesis

Reinhard Schultz

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Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions—isovariant and equivariant—often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

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 2 (2006), 739-762.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796543

Digital Object Identifier
doi:10.2140/agt.2006.6.739

Mathematical Reviews number (MathSciNet)
MR2240914

Zentralblatt MATH identifier
1173.55300

Subjects
Primary: 55P91: Equivariant homotopy theory [See also 19L47] 57S17: Finite transformation groups
Secondary: 55R91: Equivariant fiber spaces and bundles [See also 19L47] 55S15: Symmetric products, cyclic products 55S91: Equivariant operations and obstructions [See also 19L47]

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

Citation

Schultz, Reinhard. Isovariant mappings of degree 1 and the Gap Hypothesis. Algebr. Geom. Topol. 6 (2006), no. 2, 739--762. doi:10.2140/agt.2006.6.739. https://projecteuclid.org/euclid.agt/1513796543


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