Gromov norm on nonpositively curved manifolds (Shi Wang, Max Planck Institute for Mathematics)

10.12.2019 10:30

Given any topological manifold, the Gromov norm is a semi-norm defined on any homology class that measures how efficiently the representing cycles can be expressed as a linear combination of singular simplicies. Despite that the Gromov norm is topological, it is closely related to the geometry of the manifold. In this talk, we focus on manifolds with nonpositive sectional curvatures. For a locally symmetric space, we show that any nontrivial class whose degree is large enough has positive Gromov norm. For a geometric rank one manifold, we give sufficient conditions to the positivity of the Gromov norm in top degree (simplicial volume).

Lieu

Room 623, Séminaire "Groupes et Géométrie"

entrée libre