Orientability and equivariant oriented cobordism of 2-torus manifolds
arXiv:1007.5105
Abstract
We give a necessary and sufficient condition for the orientability of a locally standard 2-torus manifold with a fixed point which generalizes previous results of Nakayama-Nishimura in 2005 and Soprunova-Sottile in 2013. We construct manifolds with boundary where the boundary is a disjoint union of locally standard 2-torus manifolds. We discuss equivariant oriented cobordism class of locally standard 2-torus manifolds.
17 pages, 6 figures, Previous version contained two parts. 1. Oriented cobordism of $\CP^{2k+1}$ which is available in http://arxiv.org/abs/1011.0554. 2. oriented cobordism of $\RP^{2k+1}$. The results and constructions of second part are generalized to the category of 2-torus manifolds in the present version