Mathematical Research Letters

Volume 20 (2013)

Number 5

The topology of toric origami manifolds

Pages: 885 – 906

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n5.a6

Authors

Tara S. Holm (Department of Mathematics, Cornell University, Ithaca, New York, U.S.A.)

Ana Rita Pires (Department of Mathematics, Cornell University, Ithaca, New York, U.S.A.)

Abstract

A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and coörientable folding hypersurface. We prove that the cohomology is concentrated in even degrees, and that the equivariant cohomology satisfies the Goresky, Kottwitz and MacPherson description. Finally, we show that toric origami manifolds with coörientable folding hypersurface provide a class of examples of Masuda and Panov’s torus manifolds.

2010 Mathematics Subject Classification

Primary 53D20. Secondary 55N91, 57R91.

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