Isometric Lie 2-group actions on Riemannian groupoids
JS Herrera-Carmona, F Valencia - The Journal of Geometric Analysis, 2023 - Springer
We study isometric actions of Lie 2-groups on Riemannian groupoids by exhibiting some of
their immediate properties and implications. Firstly, we prove an existence result which …
their immediate properties and implications. Firstly, we prove an existence result which …
On gauge theory and parallel transport in principal 2-bundles over Lie groupoids
A Chaudhuri - arXiv preprint arXiv:2411.00814, 2024 - arxiv.org
We investigate an interplay between some ideas in traditional gauge theory and certain
concepts in fibered categories. We accomplish this by introducing a notion of a principal Lie …
concepts in fibered categories. We accomplish this by introducing a notion of a principal Lie …
Parallel transport on a Lie 2-group bundle over a Lie groupoid along Haefliger paths
S Chatterjee, A Chaudhuri - arXiv preprint arXiv:2309.05355, 2023 - arxiv.org
We prove a Lie 2-group torsor version of the well-known one-one correspondence between
fibered categories and pseudofunctors. Consequently, we obtain a weak version of the …
fibered categories and pseudofunctors. Consequently, we obtain a weak version of the …
PB-groupoids vs VB-groupoids
A Garmendia, F Cattafi - arXiv preprint arXiv:2406.06259, 2024 - arxiv.org
arXiv:2406.06259v1 [math.DG] 10 Jun 2024 Page 1 arXiv:2406.06259v1 [math.DG] 10 Jun
2024 PB-Groupoids vs VB-Groupoids Francesco Cattafi *‡ Alfonso Garmendia †‡ June 11 …
2024 PB-Groupoids vs VB-Groupoids Francesco Cattafi *‡ Alfonso Garmendia †‡ June 11 …
The Chern-Weil-Lecomte characteristic map for -algebras
JS Herrera-Carmona, C Ortiz - arXiv preprint arXiv:2306.04465, 2023 - arxiv.org
In this paper we extend the Chern-Weil-Lecomte characteristic map to the setting of $ L_
{\infty} $-algebras. In this general framework, characteristic classes of $ L_ {\infty} $-algebra …
{\infty} $-algebras. In this general framework, characteristic classes of $ L_ {\infty} $-algebra …
Morse theory on Lie groupoids
FV Quintero - 2024 - teses.usp.br
We extend classical Morse theory to the realm of Lie groupoids and their differentiable
stacks. This allows us to obtain both topological and geometrical information of the singular …
stacks. This allows us to obtain both topological and geometrical information of the singular …
Connections on Lie groupoids and Chern–Weil theory
I Biswas, S Chatterjee, P Koushik… - … in Mathematical Physics, 2024 - World Scientific
Let 𝕏=[X 1⇉ X 0] be a Lie groupoid equipped with a connection, given by a smooth
distribution ℋ⊂ TX 1 transversal to the fibers of the source map. Under the assumption that …
distribution ℋ⊂ TX 1 transversal to the fibers of the source map. Under the assumption that …