Title: Topological classification of torus manifolds which have codimension one extended actions
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 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 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.