Acta Mathematica Hungarica
Volume/Issue:
Volume 125: Issue 3
On nonnegatively curved 4-manifolds with discrete symmetry
Authors:
J. Kim Korea Advanced Institute of Science and Technology Department of Mathematical Sciences Kusong-dong, Yusong-gu, Taejon 305-701 Korea

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H. Lee Korea Advanced Institute of Science and Technology Department of Mathematical Sciences Kusong-dong, Yusong-gu, Taejon 305-701 Korea

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Pages:
201–208
Online Publication Date:
23 Oct 2009
Publication Date:
01 Nov 2009
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-009-8237-4
Keywords:
nonnegatively curved 4-manifold; effective finite group action; 53C15
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Abstract  

Let M be the closed, simply connected, 4-manifold with nonnegative sectional curvature, called a nonnegatively curved 4-manifold, with an effective and isometric Zm-action for a positive integer m ≧ 617. Assume that Zm 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 Zm has at most one two-dimensional component, then M is homeomorphic to S4, #il=1S2 × S2, l = 1, 2, or #jk = 1 ± CP2, k = 1, 2, 3, 4, 5. The main strategy of this paper is to give an upper bound of the Euler characteristic χ(M) under the homological assumption of a Zm-action as above by using the Lefschetz fixed point formula.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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