101 citations · 504 across the 26 of their papers we have counts for
14 papers · 1 filter
A geometric characterization of -manifolds and the Frobenius theorem
Henrique Bursztyn, Miquel Cueca, Rajan Amit Mehta
This paper studies graded manifolds with local coordinates concentrated in non-negative degrees. We provide a canonical description of these objects in terms of classical geometric…
Modules and representations up to homotopy of Lie -algebroids
Madeleine Jotz Lean, Rajan Amit Mehta, Theocharis Papantonis
This paper studies differential graded modules and representations up to homotopy of Lie -algebroids, for general . The adjoint and coadjoint modules are describ…
The Atiyah class of a dg-vector bundle
Rajan Amit Mehta, Mathieu Stiénon, Ping Xu
We introduce the notions of Atiyah class and Todd class of a differential graded vector bundle with respect to a differential graded Lie algebroid. We prove that the space of vecto…
Modular Classes of Lie Groupoid Representations up to Homotopy
Rajan Amit Mehta
We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this clas…
Double Lie algebroids and representations up to homotopy
Alfonso Gracia-Saz, Madeleine Jotz Lean, Kirill C. H. Mackenzie +1
We show that double Lie algebroids, together with a chosen linear splitting, are equivalent to pairs of 2-term representations up to homotopy satisfying compatibility conditions wh…
Symplectic structures on the integration of exact Courant algebroids
Rajan Amit Mehta, Xiang Tang
We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a "Lagrangi…