Morse Theory and Concurrency

The work is intended to provide some insight about concurrency theory using ideas from geometry and algebraic topology. We define a topological space containing all traces of execution of the computer program and the information about how time flows. This is the main difference with standard topological reasoning in which there is no information about relation "in time" among points. The main task is to define equivalence of paths reflecting execution of a program. We use the notion of homotopy history equivalence relation. The model space considered in this work is a differentiable manifold with piecewise-smooth boundary. Our aim is to identify the equivalence classes with the critical points of a certain Morse function