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Topology/Geometry Seminar
Friday, April 17, 2009
4:00 pm,
260 Hawthorn
Peter Bubenik
Cleveland State University
Models and van Kampen theorems for directed homotopy theory.
Abstract: Motivated by problems in concurrent computing, one is led to study spaces in which only certain paths are allowed. In particular, the execution paths in the state space are not reversible. Abstractly, we have a topological space with certain directed paths. Directed paths that are homotopic in a directed sense correspond to execution paths that are equivalent: for any input they will give the same output.
Directed homotopy theory has some immediate surprises. There are simple contractible partially-ordered spaces in which there are directed paths that are not (directed) homotopic. A main object of study is the fundamental category, which is the directed analog of the fundamental groupoid. I will construct some models and show some van Kampen theorems for this theory.
We meet weekly on Friday afternoons at Penn State Altoona (and sometimes at Penn State University Park). If you are interested in giving a talk in our seminar please contact one of the coordinators for the Spring 2009 semester: Wojtek Dorabiala and Aissa Wade.
