This article is cited in 5 papers

Toric origami manifolds and multi-fans

Mikiya Masuda^a, Seonjeong Park<sup>b

a</sup> Department of Mathematics, Osaka City University, Osaka, Japan
^b Division of Mathematical Models, National Institute for Mathematical Sciences, Daejeon, Korea

Abstract: The notion of a toric origami manifold, which weakens the notion of a symplectic toric manifold, was introduced by A. Cannas da Silva, V. Guillemin and A. R. Pires. They showed that toric origami manifolds bijectively correspond to origami templates via moment maps, where an origami template is a collection of Delzant polytopes with some folding data. Like a fan is associated to a Delzant polytope, a multi-fan introduced by A. Hattori and M. Masuda can be associated to an oriented origami template. In this paper, we discuss their relationship and show that any simply connected compact smooth $4$-manifold with a smooth action of $T^2$ can be a toric origami manifold. We also characterize products of even dimensional spheres which can be toric origami manifolds.

UDC: 515.165

Received in May 2013

Language: English

DOI: 10.1134/S0371968514030182

 English version: Proceedings of the Steklov Institute of Mathematics, 2014, 286, 308–323

Bibliographic databases:

• 
• 
• 
•