On nonnegatively curved 4-manifolds with discrete symmetry

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Let M be the closed, simply connected, 4-manifold with nonnegative sectional curvature, called a nonnegatively curved 4-manifold, with an effective and isometric Z (m) -action for a positive integer m a parts per thousand 61(7). Assume that Z (m) acts trivially on the homology of M. The goal of this short paper is to prove that if the fixed point set of any nontrivial element of Z (m) has at most one two-dimensional component, then M is homeomorphic to S (4), # (i) (l) =1S (2) x S (2), l = 1, 2, or # (j) (k) = 1 +/- CP (2), k = 1, 2, 3, 4, 5. The main strategy of this paper is to give an upper bound of the Euler characteristic chi(M) under the homological assumption of a Z (m) -action as above by using the Lefschetz fixed point formula.
Publisher
SPRINGER
Issue Date
2009-11
Language
English
Article Type
Article
Keywords

SIMPLY CONNECTED 4-MANIFOLDS; CIRCLE ACTIONS; TOPOLOGY; CURVATURE

Citation

ACTA MATHEMATICA HUNGARICA, v.125, no.3, pp.201 - 208

ISSN
0236-5294
DOI
10.1007/s10474-009-8237-4
URI
http://hdl.handle.net/10203/93581
Appears in Collection
MA-Journal Papers(저널논문)
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