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Symmetric group actions on homotopy S 2 × S 2
Authors:Ximin Liu  Hongxia Li
Institution:(1) Dalian University of Technology, Dalian, P.R. China
Abstract:Let X be a closed smooth 4-manifold which is homotopy equivalent to S 2 × S 2. In this paper we use Seiberg-Witten theory to prove that if X admits a spin symmetric group S 4 action of even type with b 2 + (X/S 4) = b 2 + (X), then as an element of R (S 4), Ind S4 D X = k 1 (1 − θ) + k 21 − ψ2) for some integers k 1 and k 2, where 1, θ, ψ1, ψ2 are irreducible characters of S 4 of degree 1, 1, 3, and 3 respectively. Authors’ address: Ximin Liu and Hongxia Li, Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P.R. China
Keywords:2000 Mathematics Subject Classification: 57R57  57M60  57S25  57S17
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