| Abstract: |
Given a smooth manifold and tuples of basepoints, we define a Morse-type A infinity-algebra, called the based multiloop algebra, as a graded generalization of the braid skein algebra due to Morton-Samuelson. For example, when the braid skein algebra is the Type A double affine Hecke algebra (DAHA). The A infinity-operations couple Morse gradient trees on a based loop space with Chas-Sullivan type string operations. We show that, after a certain base change, it is equivalent to the wrapped higher-dimensional Heegaard Floer A infinity-algebra of disjoint cotangent fibers. This is joint work with Ko Honda, Roma Krutowski, and Yin Tian. |
