Algebraic & Geometric Topology

Isovariant mappings of degree 1 and the Gap Hypothesis

Reinhard Schultz

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Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions—isovariant and equivariant—often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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

Blakers–Massey Theorem deleted cyclic reduced product diagram category diagram cohomology equivariant mapping Gap Hypothesis group action homotopy equivalence isovariant mapping normally straightened mapping


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.

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