Home > RHUMJ > Vol. 11 (2010) > Iss. 2

#### Article Title

#### Abstract

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.

#### Sponsor

Robert Lipshitz, Department of Mathematics, Columbia University lipshitz@math.columbia.edu

#### Recommended Citation

Jang, Jin Woo; Vishnepolsky, Rachel; and Wang, Xuran
(2010)
"Computing Fixed Point Floer Homology,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 11
:
Iss.
2
, Article 9.

Available at:
https://scholar.rose-hulman.edu/rhumj/vol11/iss2/9