## 幾何学コロキウム: Two features of Hirzebruch $\chi_y$ genus, their applications and generalizations

2013年 　 4月 26日 16時 30分 ～ 2013年 　 4月 26日 18時 00分

3-204

Dr. Ping Li (早稲田大学）

Title: Two features of Hirzebruch $\chi_y$ genus, their applications and generalizations

Abstract: The Hirzebruch $\chi_y$-genus, which was introduced by Hirzebruch in
mid-1950s, has two important features: rigidity property and "-1"-phenomenon.
Rigidity means the invariance of the equivariant $\chi_y$-genus under one-parameter
group actions. "-1"-phenomenontells us that the coefficients of the Taylor expansion
of $\chi_y$-genus at y=-1 have explicit expressions. These two features have been
observed, explicitly or implicitly, in many independent articles which have various
backgrounds. In this talk, I will review some previous results and present some of
my applications and generalizations.