幾何学コロキウム：On higher Hochschild homology of a wedge of circles（Christine Vespa氏，Université de Strasbourg）

開催日時

2019年6月14日 16時30分 ～ 2019年6月14日 18時00分

場所

理学部３号館３－２０４室

講演者

Christine Vespa （Université de Strasbourg）

タイトル： On higher Hochschild homology of a wedge of circles

アブストラクト：
Higher Hochschild homology is a generalization of classical Hochschild homology for rings introduced by Pirashvili in 2000. Recently, Turchin and Willwacher computed higher Hochschild homology of a finite wedge of circles with coefficients in the Loday functor associated to the ring of dual numbers over the rationals. In particular, they obtained linear representations of the groups Out(F_n) which do not factorize through GL(n,Z).

In this talk, I will begin by recalling what is Hochschild homology and higher Hochschild homology. Then I will explain how viewing higher Hochschild homology of a finite wedge of circles as a functor on the category of free groups provides a conceptual framework which allows powerful tools such as exponential functors and polynomial functors to be used. In particular, this allows the generalization of the results of Turchin and Willwacher; this gives rise to new linear representations of Out(F_n) which do not factorize through GL(n,Z).

(This is joint work with Geoffrey Powell.)