1-cocycles on the fatgraph complex ( Yusuke Kuno, Tsuda College, Japan)

25.10.2016 15:30

The fatgraph complex associated to an oriented surface can be seen as a combinatorial model for the Teichmuller space and the mapping class group action on it. It's study has a number of applications to the cohomology of the mapping class group and the moduli space.

In 2008, Morita and Penner gave a 1-cocycle on the fatgraph complex, which provides an explicit cocycle for the extended first Johnson homomorphism. Since then there have been known several other constructions of 1-cocycles related to twisted cohomology classes of the mapping class group.

In this talk, we first review these 1-cocycles. Then we discuss a certain secondary object coming from the comparison of the Morita-Penner cocycle and a cocycle introduced by Penner, Turaev and the speaker in 2013. We will also mention a construction of spin structures on a once bordered surface from a trivalent fatgraph spine on it, and relate this construction with our secondary object.

Lieu

Bâtiment: Battelle

Villa Battelle, Séminaire "Groupes de Lie et espaces des modules"

entrée libre