69 citations · 106 across the 11 of their papers we have counts for
14 papers
Homotopy of representations up to homotopy
Olivier Brahic, Pedro Frejlich
We propose a general definition of morphism of representations up to homotopy of Lie algebroids, which is be mandated by the requirement that taking cohomology with coefficients in…
Lie groupoids and their natural transformations
Olivier Brahic, Dion Pasievitch
We discuss natural transformations in the context of Lie groupoids, and their infinitesimal counterpart. Our main result is an integration procedure that provides smooth natural tr…
Hessian Riemannian gradient flows in convex programming
Felipe Alvarez, Jérôme Bolte, Olivier Brahic
Motivated by a constrained minimization problem, it is studied the gradient flows with respect to Hessian Riemannian metrics induced by convex functions of Legendre type. The first…
-actions of Lie algebroids
Olivier Brahic, Marco Zambon
We consider homotopy actions of a Lie algebroid on a graded manifold, defined as suitable -algebra morphisms. On the "semi-direct product" we construct a homological ve…
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…
Integration of Coupling Dirac Structures
Olivier Brahic, Rui Loja Fernandes
Coupling Dirac structures are Dirac structures defined on the total space of a fibration, generalizing hamiltonian fibrations from symplectic geometry, where one replaces the sympl…