中科院数学与系统科学研究院
数学研究所
拓扑研讨班
报告人：黄瑞芝 博士 (中科院数学院)
题 目：Stringc structures, modular invariants and non-abelian group actions
时 间：2019.12.23（星期一）, 10:30-11:30
地 点：数学院南楼N902室
摘 要：Spin structure and its higher analogies play important roles in index theory and mathematical physics. In particular, Witten genera for String manifolds have nice geometric implications. As a generalization of the work of Chen-Han-Zhang (2011), we introduce the general Stringc structures based on the algebraic topology of Spinc groups. It turns out that there are infinitely many distinct universal Stringc structures indexed by the infinite cyclic group. We then construct a family of the so-called generalized Witten genera for Spinc manifolds, the geometric implications of which can be exploited in the presence of Stringc structures. As in the un-twisted case studied by Witten, Liu, etc, in our context there are also integrality, modularity, and vanishing theorems for effective non-abelian group actions. We will give some applications of our vanishing theorem.
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