Abstract: "Cubical homotopy theory: a beginning", by. J.F. Jardine
This paper gives a closed model structure for the category of cubical
sets, suitably defined, and displays an equivalence of the associated
homotopy category with the ordinary homotopy category of topological
spaces, or simplicial sets.
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 effectively
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.
Department of Mathematics
University of Western Ontario
London, Ontario N6A 5B7
Canada
URL: http://www.math.uwo.ca/~jardine/papers/