Cup Product Issues in the Mapping Cone Morse Theory
Time: 2026-09-08
Published By: He Liu
Speaker(s): Hao Zhuang (BICMR)
Time: 15:00-16:00 September 11, 2026
Venue: Room 77201, Jingchunyuan 78, BICMR
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.
