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Topology/Geometry Seminar
Friday, April 24, 2009
4:00 pm,
260 Hawthorn
Mark Johnson
Penn State Altoona
On homotopy invariance for algebras over colored props.
Abstract: In joint work with Donald Yau, colored PROPs and their algebras have been given `projective' Quillen model category structures. Recall that PROPs are the more general cousins of operads, so a large variety of structured objects can be described as algebras over colored PROPs. Among the motivations for extending such a homotopy theory to the realm of colored PROPs is the fact that we get a homotopy invariant version of Segal's approach to Topological Conformal Field Theory. This follows since Segal's construction gluing `pairs of alien pants', thinking of cobordisms as morphisms between conformal disks of various radii, with composition given by conformal gluing, gives rise to a colored PROP. Along the way, we found a nice presentation of PROPs as monoidal monoids, and built on work of Berger and Moerdijk about homotopy theory for (colored) operads and their algebras.
We meet weekly on Friday afternoons at Penn State Altoona (and sometimes at Penn State University Park). If you are interested in giving a talk in our seminar please contact one of the coordinators for the Spring 2009 semester: Wojtek Dorabiala and Aissa Wade.
