Periodic maps of composite order on positive definite 4–manifolds

Edmonds, Allan L

doi:10.2140/gt.2005.9.315

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Periodic maps of composite order on positive definite 4–manifolds

Allan L Edmonds

Geometry & Topology 9 (2005) 315–339

DOI: 10.2140/gt.2005.9.315

arXiv: math.GT/0205110

Abstract

The possibilities for new or unusual kinds of topological, locally linear periodic maps of non-prime order on closed, simply connected 4–manifolds with positive definite intersection pairings are explored. On the one hand, certain permutation representations on homology are ruled out under appropriate hypotheses. On the other hand, an interesting homologically nontrivial, pseudofree, action of the cyclic group of order 25 on a connected sum of ten copies of the complex projective plane is constructed.

Keywords

periodic map, 4–manifold, positive definite, permutation representation, pseudofree

Mathematical Subject Classification 2000

Primary: 57S17

Secondary: 57S25, 57M60, 57N13

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Publication

Received: 8 July 2004

Revised: 23 January 2005

Accepted: 21 February 2005

Published: 23 February 2005

Proposed: Ronald Fintushel

Seconded: Walter Neumann, Ronald Stern

Authors

Allan L Edmonds
Department of Mathematics Indiana University Bloomington Indiana 47405 USA

Volume 9, issue 1 (2005)