## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Pre-Symplectic Structure on the Space of Connections

Tosiaki Kori

#### Abstract

Let $X$ be a four-manifold with boundary three-manifold $M$. We shall describe (i) a pre-symplectic structure on the sapce $\mathcal{A}(X)$ of connections on the bundle $X\times \mathrm{SU}(n)$ that comes from the canonical symplectic structure on the cotangent space $T^{\ast}\mathcal{A}(X)$. By the boundary restriction of this pre-symplectic structure we obtain a pre-symplectic structure on the space $\mathcal{A}^{\flat}_0(M)$ of flat connections on $M\times \mathrm{SU}(n)$ that have null charge.

#### Article information

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436815743

Digital Object Identifier
doi:10.7546/giq-16-2015-188-194

Mathematical Reviews number (MathSciNet)
MR3363844

Zentralblatt MATH identifier
1350.53110

#### Citation

Kori, Tosiaki. Pre-Symplectic Structure on the Space of Connections. Proceedings of the Sixteenth International Conference on Geometry, Integrability and Quantization, 188--194, Avangard Prima, Sofia, Bulgaria, 2015. doi:10.7546/giq-16-2015-188-194. https://projecteuclid.org/euclid.pgiq/1436815743