报告人：杨会军（河南大学）

邀请人：熊跃山

报告时间：2021年5月29日（星期六）10:10-11:40

报告地点：科技楼（南楼）602室

报告题目：The existence of contact structures on 9-manifolds

报告摘要：We give necessary and sufficient conditions for a closed orientable 9-manifold M to admit an almost contact structure. The conditions are stated in terms of the Stiefel-Whitney classes of M and other more subtle homotopy invariants of M. By a fundamental result of Borman, Eliashberg and Murphy, M admits an almost contact structure if and only if M admits an over-twisted contact structure. Hence we give necessary and sufficient conditions for M to admit an over-twisted contact structure and we prove that if N is another closed 9-manifold which is homotopy equivalent to M, then M admits an over-twisted contact structure if and only if N does. In addition, for W_i(M) the i-th integral Stiefel-Whitney class of M, we prove that if W_3(M) = 0 then W_7(M) = 0. This is a joint work with Professor Diarmuid Crowley.

报告人简介：杨会军，河南大学副教授，研究方向为代数拓扑，主要研究流形上近复结构和切触结构的存在性问题。