Geometry & Topology, Vol. 9 (2005) Paper no. 10, pages 315--339.

Periodic maps of composite order on positive definite 4-manifolds

Allan L Edmonds

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

AMS subject classification. Primary: 57S17. Secondary: 57S25, 57M60, 57N14.

DOI: 10.2140/gt.2005.9.315

E-print: arXiv:math.GT/0205110

Submitted to GT on 8 July 2004. (Revised 23 January 2005.) Paper accepted 21 February 2005. Paper published 23 February 2005.

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

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