BIMSA > Tsinghua-BIMSA Symplectic Geometry Seminar Morse theory of loop spaces, Hecke algebras, and the higher-dimensional Heegaard Floer homology of cotangent fibers
Morse theory of loop spaces, Hecke algebras, and the higher-dimensional Heegaard Floer homology of cotangent fibers
Organizers
Kenji Fukaya , Honghao Gao , Hang Yuan
Speaker
Ko Honda
Time
Thursday, September 18, 2025 3:30 PM - 4:30 PM
Venue
Shuangqing-B627
Abstract
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.