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Deformation Theory Seminar

Wednesday, December 15, 2010 - 1:00pm

Ralph Kaufmann

Purdue and IAS

Location

University of Pennsylvania

DRL 4N30

We can reinterpret Gerstenhaber´s bracket in terms of a general setup involving generalized operads. In the classical example, this explains why the bracket is odd. The generalizations include odd cyclic operads and $\mathfrak k$-modular operads that appear in the Feynman transform of an operad. We give examples in each of these circumstances. In the modular context, the counterpart of the bracket is a BV operator, as we show. We then go on to give further generalizations, such as wheeled PROPs, and topological examples. One of these is related to Zwiebach´s string field theory. The master equation here drives the compactification which is that of Kimura-Stasheff-Voronov.