2023/05/06 by Xiong, Yueshan, Zeng, Haozhi
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2305.03964
The notation of torus manifolds were introduced by A. Hattori and M. Masuda. Toric manifolds, quasitoric manifolds, topological toric manifolds, toric origami manifolds and b-symplectic toric manifolds are typical examples of torus manifolds with locally standard action. Recently, L. Yu introduced a nice notion topological face ring k[Q], a generalization of Stanley-Reisener ring, for a nice manifold with corners Q. L. Yu applied polyhedral product technique developed by A. Bahri, M. Bendersky, F. Cohon and S. Gilter to show that the equivariant cohomology ring H^*T(M) of an open torus manifold M with locally standard action is isomorphic to the topological face ring of M/T under the assumption that the free part of the action is a trivial torus bundle. In this paper we show that Yu's formula holds for any open torus manifolds with locally standard action by a different appoach. In addition using our method we give an explicit formula for equivariant Stiefel-Whitney classes and Pontrjagin classes of open torus manifolds with locally standard action.