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Jean Leray

Leray Topology Group


The Leray Topology Group is built around Michael S. Weiss Humboldt Professorship, and is part of the Topology Group in Münster.

Research Area

The research of our group is loosely organised around four main projects in the areas of spaces of smooth automorphisms of disks and rational Pontryagin classes, stable homotopy theory, spaces of automorphims of manifolds generally and algebraic K- and L-theory.

In our study of diffeomorphisms of disks and rational Pontryagin classes, close connections have recently emerged with the theory of cobordism categories -- therefore with homological stability -- but also with the theory of (codimension zero) smooth embeddings -- hence with manifold calculus and more generally with functor calculus. The theory of operads here gives important background via manifold calculus and the related study of spaces of configurations in manifolds.

Operad theory also makes an apperance in the project from stable homotopy, because that project emphasises A-infty structures as a way to introduce or explain nonlinear phenomena in homological algebra.

The project on spaces automorphisms of manifolds is an old but still unfinished undertaking (begun by Weiss-Williams) with many well-known connections to L-theory and algebraic K-theory. It has many under-explored connections with functor calculus as well, specifically with the orthogonal calculus.

The study of relations between algebraic K-theory and algebraic L-theory currently focuses mainly on algebraic K-theory, topological cyclic homology and duality for very general rings or ring spectra.

All members of the Leray group contribute to these projects with their own research and expertise.

Keywords: model categories, functor calculus, homological stability, operads, relations between arithmetic geometry and algebraic topology, algebraic K-theory, surgery.

Activities

The main activities of the group comprise two weekly seminars: the Oberseminar Topologie and the (Russian-style) Leray Seminar.
Our Publications The Leray Seminar Functor Caculus Workshop (21.-26. June) Spring Functor Calculus Seminar 2015

Past Activities

The main activities of the group comprise two weekly seminars: the Oberseminar Topologie and the (Russian-style) Leray Seminar.
The Leray Seminar (Archiv) Operads in Münster (2013- 2014)


See also the Meetings and Conferences of the Topology Group for other activities in WWU Münster.

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