Equivariant maps between sphere bundles over tori and KO-degree

2005/02/24 by Mikio Furuta, M. Furuta, Furuta, M. +3 · 1 citation
Mathematics · Physics and Astronomy · #57R57 (Primary) 19L47 (Secondary) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT #msc:19L47 #msc:57R57

paper · pdf · doi:10.48550/arxiv.math/0502511

33 pages, rearranged and partially rewritten

openalex publication_date 2005/02/24 · arxiv created 2005/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show a non-existence result for some class of equivariant maps between sphere bundles over tori. The notion of equivariant KO-degree is used in the proof. As an application to Seiberg-Witten theory, for a connected closed oriented spin 4-manifold with indefinite intersection form, we have a new bound of the second Betti number by the signature and a non-negative integer determined by the quadruple cup product on the first cohomology group and some maps in KO-theory induced from the Albanese map.

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