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Deformation Theory Seminar

Wednesday, October 16, 2002 - 2:00pm

Ralph Kaufmann

MPIM - Bonn

Location

University of Pennsylvania

DRL 4C4

Recently we defined an operad based on arcs on surfaces. This operad has an explicit structure of a version of a homotopy BV operad. Furthermore there are several suboperads of this operad which are related to Chas-Sullivans' string topology and several types of cacti. These can be shown to be related to framed little discs and little discs operad respectively. Finally, there are tree representations of these suboperads which allow to lift the operad governing pre-Lie algebras to the chain level. Furthermore this picture explains the origin of a second multiplication yielding "pre-Poisson algebras" and the relation to the Hopf algebra of Connes and Kreimer.