Topology of Geometric Joins

Bárány, Imre and Holmsen, A. F. and Karasev, R. (2015) Topology of Geometric Joins. DISCRETE AND COMPUTATIONAL GEOMETRY, 53 (2). pp. 402-413. ISSN 0179-5376

Preview

Text barany.pdf Download (141kB) | Preview

Abstract

We consider the geometric join of a family of subsets of the Euclidean space. This is a construction frequently used in the (colorful) Carathéodory and Tverberg theorems, and their relatives. We conjecture that when the family has at least d + 1 sets, where d is the dimension of the space, then the geometric join is contractible. We are able to prove this when d equals 2 and 3, while for larger d we show that the geometric join is contractible provided the number of sets is quadratic in d. We also consider a matroid generalization of geometric joins and provide similar bounds in this case. © 2015, Springer Science+Business Media New York.

Actions (login required)

Edit Item