Descent for n-Bundles

Descent for n-Bundles

Tue, 07/05
15:45 		Jesse Wolfson (Northwestern) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Descent for n-Bundles
Given a Lie group $ G $, one can construct a principal $ G $-bundle on a manifold $ M $ by taking a cover $ U\to M $, specifying a transition cocycle on the cover, and then descending the trivialized bundle $ U \times G $ along the cocycle. We demonstrate the existence of an analogous construction for local $ n $-bundles for general $ n $. We establish analogues for simplicial Lie groupoids of Moore's results on simplicial groups; these imply that bundles for strict Lie $ n $-groupoids arise from local $ n $-bundles. We conclude by constructing a simple finite dimensional model of the Lie 2-group String($ n $) using cohomological data.