3/25/2010

Peter Landweber
Rutgers University

Topological complexity, Euclidean embeddings of RP(n), and the cohomology of configuration spaces of pairs of distinct points in RP(n)

This will be a report on joint work with Jesus Gonzalez, about topics related to topological complexity (TC), introduced by Michael Farber in 2003 as a numerical measure of the complexity of robot motion planning problems. TC of real projective space RP(n) coincides with the Euclidean immersion dimension of RP(n) for n different from 1, 3 and 7. For symmetric TC of RP(n), there is a close relation to the Euclidean embedding dimension of RP(n). Our current study of symmetric TC involves configuration spaces of pairs of distinct points in RP(n) and has led to a calculation of their integral cohomology groups.