Polytopal bundle theory
by
Laura Anderson
Texas A&M University
Coauthors: Nikolai Mn"ev (Steklov Institute)

A polytopal bundle is a combinatorial analog to a topological sphere bundle, in which the base space is replaced by a poset and the fibers are replaced by combinatorial types of convex polytopes. The combinatorial analog to continuity is expressed in terms of polytopal subdivision. We have recently proven that the category of polytopal bundles is equivalent to the category of piecewise-linear sphere bundles. As immediate consequences we get new topological results on various categories of combinatorial types of polytopes.

Date received: May 19, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadi-08.