In the summer of 2009, our group developed a computer program that computes Hochschild Homology, a topological invariant. While we must assume that the reader has at least encountered algebraic topology, in this paper we provide the mathematical background and motivation for our algorithm. After presenting a number of definitions, we will explain how the algorithm works. Specifically, we first define the Floer complex of two curves on surface; the resulting homology is invariant under isotopies. Then, we introduce the Fukaya category associated to a sequence of curves. Next, we define the Hochschild complex of the Fukaya category. And finally, we describe an algorithm for computing Hochschild Homology and provide some examples.
Robert Lipshitz, Department of Mathematics, Columbia University firstname.lastname@example.org
Jang, Jin Woo; Vishnepolsky, Rachel; and Wang, Xuran
"Computing Fixed Point Floer Homology,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 11
, Article 9.
Available at: http://scholar.rose-hulman.edu/rhumj/vol11/iss2/9