Algebra/Topology seminar

Speaker: Katsuhiko Kuribayashi (Shinshu University)

Title: Eilenberg-Moore spectral sequence calculations in string topology of classifying spaces. 

Abstract: String topology gives fruitful structures to the loop homology of orientable manifolds, classifying spaces of Lie groups, more general Gorenstein spaces. In this talk, we focus on the Batalin-Vilkovisky algebra (BV algebra) structure on the loop cohomology of a classifying space BG with coefficients in a field. In particular, the BV algebra structure is determined explicitly provided the cohomology of the given Lie group G is isomorphic to a polynomial algebra. The machinery for such computations is the Eilenberg-Moore spectral sequence with module derivations. Moreover, in the open-closed topological quantum field theory on a classifying space in the sense of Guldberg, the (non)triviality of a labeled whistle cobordism operation is discussed if time permits.
This talk is based on joint work with Luc Menichi (University of Angers).