The van Est homomorphism for strict Lie 2-groups
Differential Geometry
2025-10-07 v2 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
We construct a van Est map for strict Lie 2-groups from the Bott-Shulman-Stasheff double complex of the strict Lie 2-group to the Weil algebra of its associated strict Lie 2-algebra. We show that, under appropriate connectedness assumptions, this map induces isomorphisms in cohomology. As an application, we differentiate the Segal 2-form on the loop group.
Cite
@article{arxiv.2405.09969,
title = {The van Est homomorphism for strict Lie 2-groups},
author = {Camilo Angulo and Miquel Cueca},
journal= {arXiv preprint arXiv:2405.09969},
year = {2025}
}