Suppose we are given a mapping class on a surface with boundary, s.t. the boundary is fixed. We will show how to assign to such object two invariants. The first one is an A-infinity bimodule, which is defined using intersections of curves and their images on a surface. The second is fixed point Floer homology, which counts fixed points of a map representing the mapping class. We will conclude with stating a conjectural connection between these two invariants.