50 citations · 153 across the 15 of their papers we have counts for
15 papers
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…
The Chern-Weil-Lecomte characteristic map for -algebras
Juan Sebastian Herrera-Carmona, Cristian Ortiz
In this paper we extend the Chern-Weil-Lecomte characteristic map to the setting of -algebras. In this general framework, characteristic classes of -algebra…
Complex Dirac structures with constant real index on flag manifolds
Cristian Ortiz, Carlos Varea
In this paper we describe all invariant complex Dirac structures with constant real index on a maximal flag manifold in terms of the roots of the Lie algebra which defines the flag…
Morse theory on Lie groupoids
Cristian Ortiz, Fabricio Valencia
In this paper we introduce Morse Lie groupoid morphisms and study their main properties. We show that this notion is Morita invariant which gives rise to a well defined notion of M…
Quotients of multiplicative forms and Poisson reduction
Alejandro Cabrera, Cristian Ortiz
In this paper we study quotients of Lie algebroids and groupoids endowed with compatible differential forms. We identify Lie theoretic conditions under which such forms become basi…
On the Lie 2-algebra of sections of an LA-groupoid
Cristian Ortiz, James Waldron
In this work we introduce the category of multiplicative sections of an $\la$-groupoid. We prove that this category carries natural strict Lie 2-algebra structures, which are Morit…
Morita equivalences of vector bundles
Matias del Hoyo, Cristian Ortiz
We study vector bundles over Lie groupoids, known as VB-groupoids, and their induced geometric objects over differentiable stacks. We establish a fundamental theorem that character…
Integration of 2-term representations up to homotopy via 2-functors
Cristian Ortiz, Olivier Brahic
Given a representation up to homotopy of a Lie algebroid on a 2-term complex of vector bundles, we define the corresponding holonomy as a strict 2-functor from a Weinstein path 2-g…
Obstructions to the integrability of VB-algebroids
Olivier Brahic, Alejandro Cabrera, Cristian Ortiz
VB-groupoids can be thought of as vector bundle objects in the category of Lie groupoids. Just as Lie algebroids are the infinitesimal counterparts of Lie groupoids, VB-algebroids…
VB-algebroid morphisms and representations up to homotopy
Thiago Drummond, Madeleine Jotz Lean, Cristian Ortiz
We show in this paper that the correspondence between -term representations up to homotopy and -algebroids, established by Gracia-Saz and Mehta, holds also at the…
Multiplicative Dirac structures
Cristian Ortiz
In this paper we introduce multiplicative Dirac structures on Lie groupoids, providing a unified framework to study both multiplicative Poisson bivectors (i.e., Poisson group(oid)s…
Foliated groupoids and their infinitesimal data
Madeleine Jotz, Cristian Ortiz
In this work, we study Lie groupoids equipped with multiplicative foliations and the corresponding infinitesimal data. We determine the infinitesimal counterpart of a multiplicativ…
B-field transformations of Poisson groupoids
Cristian Ortiz
In this work we study B-field transformations of multiplicative Poisson bivectors on a Lie groupoid G. We are concerned with B-fields given by multiplicative closed 2-forms on G. W…
Linear and multiplicative 2-forms
Henrique Bursztyn, Alejandro Cabrera, Cristian Ortiz
We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of mu…
Multiplicative Dirac structures on Lie groups
Cristian Ortiz
We study multiplicative Dirac structures on Lie groups. We show that the characteristic foliation of a multiplicative Dirac structure is given by the cosets of a normal Lie subgrou…