Research Seminar
(Wednesday, May 29, 2002)
2:15 p.m.
Math 105
Rick Jardine
Department of Mathematics
University of Western Ontario
Cubical homotopy theory: a beginning
A cubical complex is the analogue of a simplicial complex, but
built with cubes rather than tetrahedra. Cubical complexes appeared in
the early descriptions of homology theory and combinatorial homotopy
theory in the middle of the twentieth century, but development of the
subject area stopped as simplicial sets became the dominant
combinatorial model for homotopy theory as a result of the work of Kan
and later Quillen. Cubical complexes have recently resurfaced as objects
of fundamental interest in Pratt's theory of higher dimensional automata
in concurrency theory, and have appeared in some discussions of higher
categorical structures. This talk will display an approach to the still
unanswered question of the existence of an intrinsic combinatorial
homotopy theory for these objects.
The speaker is a candidate for the position of Head, Department of Mathematics.
