3 papers
math.DG2026
Geometric differentiation of simplicial manifolds
Alejandro Cabrera, Matias del Hoyo
We provide a complete geometric solution to the problem of differentiating simplicial manifolds, extending classical Lie theory and complementing existing homotopical and formal ap…
math.CT2024
Higher Vector Bundles
Matias del Hoyo, Giorgio Trentinaglia
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…
math.DG2024
On the cohomology of differentiable stacks
Matias del Hoyo, Cristian Ortiz, Fernando Studzinski
Morita equivalence classes of Lie groupoids serve as models for differentiable stacks, which are higher spaces in differential geometry, generalizing manifolds and orbifolds. Repre…