The Grothendieck Teichmuller lie algebra and homotopy equivalences of configuration spaces
The Grothendieck Teichmuller lie algebra and homotopy equivalences of configuration spaces

John Jones, Warwick University
Fine Hall 322
The Grothendieck  Teichmuller Lie algebra grt is a Lie algebra, over the rational numbers Q, which is clearly very interesting and equally clearly not very wellunderstood. It crops up in many different areas of mathematics. In this talk I will explain how the Lie algebra grt is related to the space of homotopy equivalences of the configuration spaces F(k, R^n) and F(k, S^n). Here F(k,X) is the space of k distinct ordered points in the topological space X. Much of the talk will be devoted to explaining, in as concrete a way as possible, the background needed for the statements of the results. I will also try to explain one or two of the key ideas in the proofs.