ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXVI, 2 (2007)
p. 247 - 256
On Symmetric Group S3 Actions on Spin 4-manifolds
Ximin Liu and Hongxia Li
Abstract.
Let X be a smooth, closed, connected spin 4-manifold with
b1(X) = 0 and non-positive signature
s(X). In this paper
we use Seiberg-Witten theory to prove that if X admits an odd
type symmetric group S3 action preserving the spin structure,
then
b2+(X) ³
|s(X)|/8 +3
under some non-degeneracy
conditions. We also obtain some information about
Ind~S3D, where
~S3 is the extension of
S3 by Z2.
Keywords:
spin 4-manifolds, symmetric group, Seiberg-Witten theory.
AMS Subject classification. 57R57, 57M60, 57R15.
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