Topological classification of torus manifolds which have codimension one extended actions

Details Topological classification of torus manifolds which have codimension one extended actions Topological classification of torus manifolds which have codimension one extended actions

2009-06-07

arxiv.org/abs/0906.1335v2

Algebr. Geom. Topol. 11(5) (2011), 2655-2679

Mathematics

Algebraic Topology

20 pages

Scientific paper

A toric manifold is a compact non-singular toric variety equipped with a natural half-dimensional compact torus action. A torus manifold is an oriented, closed, smooth manifold of dimension $2n$ with an effective action of a compact torus $T^{n}$ 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 $\mM$ in the family of torus manifolds with codimension one extended actions, and we give a topological classification of $\mM$. 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 even if its orbit spaces are highly structured. 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.

Affiliated with

Also associated with

No associations

Rating

Topological classification of torus manifolds which have codimension one extended actions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Topological classification of torus manifolds which have codimension one extended actions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological classification of torus manifolds which have codimension one extended actions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-369989