Witt pseudomanifolds, Gysin homomorphisms in K-homology and a formula for the Goresky-MacPherson G-signature

Paolo Piazza  (Sapienza University of Rome)

15:00-16:00, July 13, 2026   闵行校区数学楼 102

Abstract:

Gysin homomorphisms in K-theory and K-homology and their functoriality properties have played a major role in index theory (on smooth manifolds, Lipschitz manifolds and foliations). Using stable homotopy theory, Banagl has defined Gysin homomorphisms in K-homology for Witt pseudomanifolds and proved that they preserve the Sullivan-Siegel orientation class. Examples of Witt pseudomanifols include complex projective varieties. In this talk I will explain an analytic approach to these results, using KK-theory and the signature operator. This analytic approach will in fact allow for much more general results and, moreover, it is fully compatible with the topological approach. I will also discuss an application of these techniques to the formulation and proof of an Atiyah-Segal-Singer formula for the Goresky-MacPherson G-signature of a Witt pseudomanifold. The first part of the talk is joint work with Pierre Albin and Markus Banagl. The second part, on the G-signature formula, is joint work with Markus Banagl and Eric Leichtnam. These articles are available on the arxiv.

About the speaker:

Paolo Piazza 教授现任意大利罗马大学（Sapienza University of Rome ）数学系教授，是非交换几何与全局分析领域的国际知名学者。他 的研究广泛而深入，主要集中在高阶指数理论、K-理论、循环同 调，以及它们在流形拓扑与几何中的应用。Piazza 教授不仅在经典 光滑流形的指数理论上造诣深厚，更特别擅长处理具有复杂结构的 几何体，如带边流形、带角流形以及带有群作用的流形。通过引入 创新的代数与同调工具，他在研究狄拉克算子、拓扑障碍问题，以 及解决复杂边界流形的指数定理与 Fredholm障碍等方面，做出了众多系统且开创性的贡献。

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