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VOL. 16 | 2015 Pre-Symplectic Structure on the Space of Connections
Tosiaki Kori

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

## 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.

## Information

Published: 1 January 2015
First available in Project Euclid: 13 July 2015

zbMATH: 1350.53110
MathSciNet: MR3363844

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