Cup products in bounded cohomology of the free group via aligned cochains (Sofia Amontova, Université de Genève)

13.10.2020 10:30

Despite its wide range of uses in geometric group theory as well as in the geometry and topology of manifolds, bounded cohomology turns out to be hard to compute in general. Even for the case of a non-abelien free group, while something can be said about the bounded cohomology group with trivial real coefficients up to degree 3, for higher degrees it is still not known whether it vanishes or not.

Recently, examples of trivial cup products in the bounded cohomology of degree 4 of the free group have been constructed by Bucher and Monod, Heuer and Facio.
In this talk, we not only extend examples of trivial cup products for this case considerably but also generate examples of trivial cup products in the case of arbitrary higher degree. The result suggests that conjecturally for degrees greater than 3, the bounded cohomology of the free group should vanish.
In particular, for the construction of our examples, we explain the notion of Delta-decomposable quasimorphisms by Heuer and the role of aligned cochains, a construction by Bucher and Monod.

This is joint work with Michelle Bucher.

Lieu

Salle 623
Séminaire Groupes et Géométrie

entrée libre