Previous issue ·  Next issue ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Moscow Mathematical Journal

Volume 13, Issue 1, January–March 2013  pp. 57–98.

Topological Toric Manifolds

Authors Hiroaki Ishida (1), Yukiko Fukukawa (2), and Mikiya Masuda (2)
Author institution: (1) Osaka City University Advanced Mathematical Institute, Sumiyoshi-ku, Osaka 558-8585, Japan
(2) Department of Mathematics, Osaka City University, Sumiyoshi-ku, Osaka 558-8585, Japan

Summary: 

We introduce the notion of a topological toric manifold and a topological fan and show that there is a bijection between omnioriented topological toric manifolds and complete non-singular topological fans. A topological toric manifold is a topological analogue of a toric manifold and the family of topological toric manifolds is much larger than that of toric manifolds. A topological fan is a combinatorial object generalizing the notion of a simplicial fan in toric geometry.

Prior to this paper, two topological analogues of a toric manifold have been introduced. One is a quasitoric manifold and the other is a torus manifold. One major difference between the previous notions and topological toric manifolds is that the former support a smooth action of an S1-torus while the latter support a smooth action of a ℂ*-torus. We also discuss their relation in details.

2010 Mathematics Subject Classification. Primary: 53D20, 57S15; Secondary: 14M25.


Back to Issue TOC    Full-Text PDF