This monograph presents an application of concepts and methods from
algebraic topology to models of concurrent processes in computer
science and their analysis.
Taking well-known discrete models for concurrent processes in resource
management as a point of departure, the book goes on to refine
combinatorial and topological models. In the process, it develops tools
and invariants for the new discipline directed algebraic topology,
which is driven by fundamental research interests as well as by
applications, primarily in the static analysis of concurrent programs.
The state space of a concurrent program is described as a
higher-dimensional space, the topology of which encodes the essential
properties of the system. In order to analyse all possible executions in
the state space, more than "just" the topological properties have to be
considered: Execution paths need to respect a partial order given by the
time flow. As a result, tools and concepts from topology have to be
extended to take privileged directions into account.
The target audience for this book consists of graduate students,
researchers and practitioners in the field, mathematicians and computer
scientists alike.