Topological classification of torus manifolds which have codimension one extended actions

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.Comment: 20 page

Hybridization-induced superconductivity from the electron repulsion on a tetramer lattice having a disconnected Fermi surface

Plaquette lattices with each unit cell containing multiple atoms are good candidates for disconnected Fermi surfaces, which are shown by Kuroki and Arita to be favorable for spin-flucutation mediated superconductivity from electron repulsion. Here we find an interesting example in a tetramer lattice where the structure within each unit cell dominates the nodal structure of the gap function. We trace its reason to the way in which a Cooper pair is formed across the hybridized molecular orbitals, where we still end up with a T_c much higher than usual.Comment: 4 pages, 6 figure