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2011 Topological classification of torus manifolds which have codimension one extended actions
Suyoung Choi, Shintarô Kuroki
Algebr. Geom. Topol. 11(5): 2655-2679 (2011). DOI: 10.2140/agt.2011.11.2655

Abstract

A toric manifold is a compact non-singular toric variety. A torus manifold is an oriented, closed, smooth manifold of dimension 2n with an effective action of a compact torus Tn having a non-empty fixed point set. Hence, a torus manifold can be thought of as a generalization of a toric manifold. In the present paper, we focus on a certain class M in the family of torus manifolds with codimension one extended actions, and we give a topological classification of M. As a result, their topological types are completely determined by their cohomology rings and real characteristic classes.

The problem whether the cohomology ring determines the topological type of a toric manifold or not is one of the most interesting open problems in toric topology. One can also ask this problem for the class of torus manifolds. Our results provide a negative answer to this problem for torus manifolds. However, we find a sub-class of torus manifolds with codimension one extended actions which is not in the class of toric manifolds but which is classified by their cohomology rings.

Citation

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Suyoung Choi. Shintarô Kuroki. "Topological classification of torus manifolds which have codimension one extended actions." Algebr. Geom. Topol. 11 (5) 2655 - 2679, 2011. https://doi.org/10.2140/agt.2011.11.2655

Information

Received: 5 November 2010; Revised: 6 August 2011; Accepted: 10 August 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1231.57031
MathSciNet: MR2846908
Digital Object Identifier: 10.2140/agt.2011.11.2655

Subjects:
Primary: 55R25
Secondary: 57S25

Rights: Copyright © 2011 Mathematical Sciences Publishers

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