Open Collections

Constant symplectic 2-groupoids

Banff International Research Station for Mathematical Innovation and Discovery

Heuristically, it is known that Courant algebroids should "integrate" to symplectic 2-groupoids, but very little of this correspondence has been developed in a precise way. I will describe in detail the case of a linear 2-groupoid equipped with a constant symplectic form, and I will explain how these "constant symplectic 2-groupoids" correspond to a certain class of Courant algebroids. The study of constant symplectic 2-groupoids is intended to be a first step toward a more general study of symplectic 2-groupoids, in analogy to how a student usually first learns about symplectic vector spaces before moving on to symplectic manifolds. Symplectic 2-groupoids are closely related to the shifted symplectic structures studied by Pantev, et al, although the definition is more "strict" in certain ways. As part of the talk, I will give some context to explain why the additional strictness is appropriate for the problem of integrating Courant algebroids.

Mathematics; Differential geometry; Topological groups, lie groups

video/mp4

Author affiliation: Smith College

2017-10-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63288

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/