Higher Vector Bundles
Category Theory
2025-05-29 v4 Differential Geometry
Abstract
We introduce higher analogs for cleavages in the context of (Kan) simplicial fibrations. We apply them to obtain geometric models for representations up to homotopy of (higher) Lie groupoids. Concretely, we set an equivalence between representations up to homotopy and simplicial vector bundles endowed with a cleavage. Our result is an incarnation of the Higher Grothendieck Correspondence, it can be seen as a relative Dold-Kan Theorem and extends earlier work of Gracia-Saz and Mehta on VB-groupoids.
Cite
@article{arxiv.2109.01062,
title = {Higher Vector Bundles},
author = {Matias del Hoyo and Giorgio Trentinaglia},
journal= {arXiv preprint arXiv:2109.01062},
year = {2025}
}
Comments
36 pages, new version with generalizations to higher Lie groupoids