Geometry & Topology

Periodic maps of composite order on positive definite 4–manifolds

Allan L Edmonds

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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.

Article information

Geom. Topol., Volume 9, Number 1 (2005), 315-339.

Received: 8 July 2004
Revised: 23 January 2005
Accepted: 21 February 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57S17: Finite transformation groups
Secondary: 57S25: Groups acting on specific manifolds 57M60: Group actions in low dimensions 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx]

periodic map 4–manifold positive definite permutation representation pseudofree


Edmonds, Allan L. Periodic maps of composite order on positive definite 4–manifolds. Geom. Topol. 9 (2005), no. 1, 315--339. doi:10.2140/gt.2005.9.315.

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