Department of Mathematics
Cells, Collisions, Curvature:
an Introduction to Combinatorial Topology
Jens Harlander
Western Kentucky University
In 1993 the Russian mathematician Anton Klyachko observed the following property which he described as "suitable for a school mathematics tournament":
Given a tesselated 2-sphere, i.e. a subdivision of the surface of the ball into regions, let a car drive around the boundary of each region in an anti-clockwise direction. The cars travel at arbitrary speed, never stop and visit each point on the boundary infinitely often. Then there must be at least two places on the sphere where complete crashes occur.
He used this result to prove the Kervaire Conjecture for torsion-free groups (which had been open for 30 years). In my talk I will discuss Klyachko's Car Crash Lemma and other properties of the 2-sphere and give applications to Combinatorial Topology and Group Theory.
All interested persons are welcome.