turkmath.org

 Let P be an n-dimensional simple convex polytope. A small cover over P is a smooth closed manifold with a locally standard $\mathbb{Z}_2^n$-action whose orbit space can be identified with P. In this talk, we give necessary conditions for a small cover to have a Spin structure.  Then we consider the case where P is a product of simplices. It turns out that when the simplices in the product have dimensions greater than 1, these conditions are also sufficient. We give necessary and sufficient conditions for the existence of a Spin structure when the product contains simplices of dimension 1. To very small cover over a product of simplices, there is an associated digraph. We also give an interpretation of this result in terms of the associated digraphs. This is a joint work with S. Kaan Gürbüzer.

Link to the seminar is:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1652598779071?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d