Cup Product Issues in the Mapping Cone Morse Theory
发布时间：2026年09月08日
浏览次数：11
发布者: He Liu
主讲人： 庄昊（数学中心）
活动时间： 从 2026-09-11 15:00 到 16:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
With the cup product on the topological construction of the Thom-Smale complex, Clausen-Tang-Tseng recently built the topological side of the de Rham mapping cone version of the Thom-Smale complex associated to a Morse function. As we know, the original Thom-Smale complex admits an analytic construction by Witten, Helffer-Sjöstrand, and Bismut-Zhang. However, due to the missing cup product structure on the analytic construction of the original Thom-Smale complex, in the mapping cone situation, the construction of the analytic side is far from a direct generalization. In this talk, we present how we realize the analytic side. Our main idea is suppressing the norm of the chosen closed form and then analyzing the mapping cone Laplacian.
