Surfaces, 3-manifolds and automorphism groups

Ziel

The scientific goal of the proposal is to answer central questions related to diffeomorphism groups of manifolds of dimension 2 and 3, and to their deformation invariant analogs, the mapping class groups. While the classification of surfaces has been known for more than a century, their automorphism groups have yet to be fully understood. Even less is known about diffeomorphisms of 3-manifolds despite much interest, and the objects here have only been classified recently, by the breakthrough work of Perelman on the Poincar\'e and geometrization conjectures. In dimension 2, I will focus on the relationship between mapping class groups and topological conformal field theories, with applications to Hochschild homology. In dimension 3, I propose to compute the stable homology of classifying spaces of diffeomorphism groups and mapping class groups, as well as study the homotopy type of the space of diffeomorphisms. I propose moreover to establish homological stability theorems in the wider context of automorphism groups and more general families of groups. The project combines breakthrough methods from homotopy theory with methods from differential and geometric topology. The research team will consist of 3 PhD students, and 4 postdocs, which I will lead.

Wissenschaftliches Gebiet

Finanzierungsplan

ERC-SG - ERC Starting Grant

Gastgebende Einrichtung

KOBENHAVNS UNIVERSITET

EU-Beitrag

€ 724 992,00

Adresse

NORREGADE 10
1165 Kobenhavn
Dänemark

Region

Danmark Hovedstaden Byen København

Aktivitätstyp

Higher or Secondary Education Establishments

Hauptforscher

Nathalie Wahl (Dr.)

Kontakt Verwaltung

Ivan Kristoffersen (Mr.)

Links

Die Organisation kontaktieren Website

Gesamtkosten

Keine Daten

Begünstigte (1)