Atlas home || Conferences | Abstracts | about Atlas

Geometric Topology II
September 29 - October 5, 2002
Inter-University Center, Dubrovnik; Department of Mathematics, University of Zagreb
Dubrovnik, Croatia

Organizers
Ivan Ivansic, University of Zagreb;, James E. Keesling, University of Florida;, Alexander N. Dranishnikov, University of Florida;, Sime Ungar, University of Zagreb

View Abstracts
Conference Homepage

The space of transversals through the space of configurations
by
Deborah Oliveros
University of Calgary
Coauthors: Montejano Luis

Abstract

Let F={A0, A1, ..., Ar} be a family of convex sets in Rn. The space of m-transversals of F, denoted Tm(F), is the subspace of the Grassmannian G*(n, m) of (free) m-planes in Rn that intersect all the members of F.

The purpose of this talk is to study the topology of Tm(F) through Crm, the polyhedron of configurations of (r+1)-points in R^m; where such a configuration is the affine equivalence class of (r+1)-ordered points in R^m that affinely generate it. The configuration space has a natural polyhedral structure with faces corresponding to what has been called order types. In particular, if r=m+1 and T_m-1(F) is empty, we shall prove that the homotopy type of T_m(F) is ruled by the set of all possible order types achieved by the m-transversals of F. We shall also prove that the set of all m-transversals in T_m(F) that intersect F

Date received: August 27, 2002

Copyright © 2002 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 # caje-59.