Topology, Algebraic Geometry, and Dynamics Seminar (TADS): How to differentiate a Lie infinity-group

Speaker:  Chris Rogers, University of Nevada

Title:  How to differentiate a Lie infinity-group

Abstract:  Lie infinity-groups are reduced simplicial manifolds which satisfy a geometric version of the Kan condition from simplicial homotopy theory. In analogy with the correspondence between finite-dimensional Lie groups and Lie algebras, the infinitesimal counterpart of a finite-dimensional Lie infinity-group is a Lie infinity-algebra. This is a finite-type graded real vector space equipped with operations which satisfy the axioms of a differential graded Lie algebra, but only up to coherent homotopy. In recent work (arXiv:2409.08957) with Jesse Wolfson (UCI), we proved that every such Lie infinity-algebra integrates to a finite-dimensional Lie infinity-group. This talk will concern the inverse operation: differentiation. We will describe a homotopically well behaved differentiation functor for Lie infinity-groups that is tractable, yet sufficiently explicit, and which bypasses the technical complications surrounding similar constructions appearing in the recent literature. This is joint work in progress with Jesse Wolfson.

Time:  Friday, November 1, 1:30pm – 2:30pm

Place:  Exploratory Hall, room 4208