Date & Time: Friday, February 12, 2015, 16:00-17:00.
Venue: Ramanujan Hall

Title: Vector fields on certain quotients of the complex Stiefel manifolds

Speaker: Shilpa Gondhali, University of Haifa

Abstract: In this talk, we will try to understand Topology of a quotient of the complex Stiefel manifold, which we call $m$-projective Stiefel manifold. More precisely, we consider quotients of complex Stiefel manifolds by finite cyclic groups whose action is induced by the scalar multiplication on the corresponding complex vector space. We will obtain a description of their tangent bundles, compute their mod $p$ cohomology and obtain estimates for their span (with respect to their standard differentiable structure). We will discuss the Pontrjagin and Stiefel-Whitney classes of these manifolds and give applications to their stable parallelizability. This is part of joint work with P. Sankaran.