Zobrazeno 1 - 10
of 58
pro vyhledávání: '"DEL HOYO, MATIAS"'
Morita equivalence classes of Lie groupoids serve as models for differentiable stacks, which are higher spaces in differential geometry, generalizing manifolds and orbifolds. Representations up to homotopy of Lie groupoids provide a higher analog of
Externí odkaz:
http://arxiv.org/abs/2410.02570
Autor:
Bursztyn, Henrique, del Hoyo, Matias
A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of action codifyin
Externí odkaz:
http://arxiv.org/abs/2309.14105
We introduce higher analogs for cleavages and flatness within the context of (Kan) simplicial fibrations, and apply them to provide geometric models for Lie groupoid representations up to homotopy. Concretely, we establish a functorial equivalence be
Externí odkaz:
http://arxiv.org/abs/2109.01062
Publikováno v:
Journal of Geometric Mechanics 14 (2022): 151-178
We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these objects are re
Externí odkaz:
http://arxiv.org/abs/2106.15403
Autor:
del Hoyo, Matias, de Melo, Mateus
Publikováno v:
Lett. Math. Phys. 2021
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization remains somehow
Externí odkaz:
http://arxiv.org/abs/2105.09760
Autor:
del Hoyo, Matias, Garcia, Daniel López
Publikováno v:
Monatshefte f\"ur Mathematik, 194(4), 811-833 (2021)
We present Hausdorff versions for Lie Integration Theorems 1 and 2 and apply them to study Hausdorff symplectic groupoids arising from Poisson manifolds. To prepare for these results we include a discussion on Lie equivalences and propose an algebrai
Externí odkaz:
http://arxiv.org/abs/2003.14364
Autor:
del Hoyo, Matias, de Melo, Mateus
Publikováno v:
Transformation Groups (2020)
Metrics on Lie groupoids and differentiable stacks have been introduced recently, extending the Riemannian geometry of manifolds and orbifolds to more general singular spaces. Here we continue that theory, studying stacky curves on Riemannian stacks,
Externí odkaz:
http://arxiv.org/abs/1906.03459
Autor:
del Hoyo, Matias, Fernandes, Rui Loja
Publikováno v:
Proceedings of the American Mathematical Society 147, 10 (2019), 4555-4561
We combine classic stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids to provide a cohomological characterization for rigidity of compact foliations on compact manifolds.
Comment: 6 pages; Th
Comment: 6 pages; Th
Externí odkaz:
http://arxiv.org/abs/1807.10748
Publikováno v:
Revista Matem\'atica Iberoamericana (2020)
In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold encodes t
Externí odkaz:
http://arxiv.org/abs/1804.00220
Autor:
del Hoyo, Matias, Stefani, Davide
Publikováno v:
Pacific J. Math. 298 (2019) 33-57
We deal with the symmetries of a (2-term) graded vector space or bundle. Our first theorem shows that they define a (strict) Lie 2-groupoid in a natural way. Our second theorem explores the construction of nerves for Lie 2-categories, showing that it
Externí odkaz:
http://arxiv.org/abs/1706.07152