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
2(ψ1 − 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 |