Dihomotopy and Concurrent Computing

Abstract

<p> Concurrent Computing has certain interesting links with Algebraic Topology. There are various geometric models for concurrent computing. We examine one geometric approach to modeling concurrency, via the notion of a locally partially ordered space. We examine a notion analogous to that of homotopy, called dihomotopy, that is compatible with a local partial order. In the category of locally partially ordered spaces and di-maps we examine the isomorphisms, which are called di-homeomorphisms. We classify all di-homeomorphic embeddings of the unit square into the Euclidean plane.</p>