## Geometry and Physics Seminar: Ping Xu

• Date: 10/27/2014
• Time: 15:00
Lecturer(s):
Ping Xu, PennState
Location:

University of British Columbia

Topic:

Rozansky--Witten-type invariants from symplectic Lie pairs

Description:

In 1997, Rozansky and Witten built new finite-type invariants of 3-manifolds from hyperkahler manifolds. It was later shown by Kontsevich and Kapranov that those invariants only depend on the holomorphic symplectic structure of the hyperkahler manifolds. Indeed Kapranov proved that these invariants may be considered as an analogue of Chern-Simons type invariants, where the Atiyah class of the underlying complex manifold plays the role of Lie bracket. In this talk, we introduce symplectic structures on "Lie pairs" of (real or complex) algebroids, encompassing homogeneous symplectic spaces, symplectic manifolds with a $\mathfrak g$-action and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds. This is a joint work with Yannick Voglaire.

Other Information:

This is a live e-seminar hosted by The University of British Columbia in ESB 4127 and broadcast at The University of Alberta in CAB 449 at 4 pm (MDT).