The Grothendieck -Teichmuller lie algebra and homotopy equivalences of configuration spaces
The Grothendieck -Teichmuller lie algebra and homotopy equivalences of configuration spaces
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John Jones, Warwick University
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 well-understood.Ìý It crops up in many differentÌýÌýareas of mathematics. ÌýIn this talkÌýI will explain how the Lie algebra grt is related to the space of homotopy equivalences of theÌýconfiguration spaces F(k, R^n) and F(k, S^n).Ìý Here F(k,X) is the space of k distinct ordered points in the topological space X.Ìý Much of the talk will be devoted to explaining, in as concrete a way as possible, theÌýbackground needed for the statements of the results.Ìý I will also try to explain one or two of the keyÌýideas in the proofs.