The van Est homomorphism for strict Lie 2-groups

2024/05/16 by Camilo Angulo, Miquel Cueca, Angulo, Camilo +1
Mathematics · #18F20 #18G45 #58A50 #58H05 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2405.09969

openalex publication_date 2024/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On the Van Est homomorphism for Lie groupoids
• The Weil algebra and the Van Est isomorphism
• A cohomology theory for Lie 2-algebras and Lie 2-groups
• Towards a new cohomology theory for strict Lie 2-groups
• Van Est differentiation and integration