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The fundamental group and Betti numbers of toric origami manifolds

Tara S Holm and Ana Rita Pires

Algebraic & Geometric Topology 15 (2015) 2393–2425
Abstract

Toric origami manifolds are characterized by origami templates, which are combinatorial models built by gluing polytopes together along facets. In this paper, we examine the topology of orientable toric origami manifolds with coorientable folding hypersurface. We determine the fundamental group. In our previous paper, we studied the ordinary and equivariant cohomology rings of simply connected toric origami manifolds. We conclude this paper by computing some Betti numbers and cohomology rings in the non-simply connected case.

Keywords
toric symplectic manifold, toric origami manifold, Delzant polytope, origami template, fundamental group, Betti numbers, cohomology
Mathematical Subject Classification 2010
Primary: 53D20
Secondary: 55N91, 57R91
References
Publication
Received: 21 July 2014
Revised: 3 December 2014
Accepted: 27 December 2014
Published: 10 September 2015
Authors
Tara S Holm
Department of Mathematics
Cornell University
571 Malott Hall
Ithaca, NY 14850-4201
USA
Ana Rita Pires
Department of Mathematics
Fordham University – Lincoln Center
113 W 60th St.
Room 813
New York, NY 10023-7414
USA