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Morse theory of loop spaces, Hecke algebras, and the higher-dimensional Heegaard Floer homology of cotangent fibers

组织者

深谷賢治 , 高鸿灏 , 袁航

演讲者

Ko Honda

时间

2025年09月18日 15:30 至 16:30

地点

Shuangqing-B627

摘要

Given a smooth closed $n$-manifold $M$ and a $\kappa$-tuple of basepoints ${\bf q}\subset M$, we define a Morse-type $A_\infty$-algebra called the based multiloop $A_\infty$-algebra and show the equivalence with the higher-dimensional Heegaard Floer $A_\infty$-algebra of $\kappa$ disjoint cotangent fibers of $T^*M$. Along the way, Chas-Sullivan type string operations and Hecke algebras will make appearances.