Theta functions, root systems and 3-manifold invariants
type: Item
instance of: scholarly article
title: Theta functions, root systems and 3-manifold invariants
zbMATH Open document ID: 0854.58012
DOI: 10.1016/0393-0440(94)00050-E
published in: Journal of Geometry and Physics
publication date: 1997-01-22T00:00:00Z
review text: The author presents an extension of the Witten theory for the quantization of the Chern-Simons action in the case of a general gauge group \(G\). He considers a Chern-Simons type action on the higher dimensional Jacobian tori \(\text{Jac}(\Sigma_g) \times \mathbb{R}\), where \(\Sigma_g\) is a Riemann surface of genus \(g\). The space \(N_{\Sigma_g} = \text{Hom}(\pi_1 (\text{Jac} (\Sigma_g)), G)/G\) of the representations of \(\pi_1(\text{Jac} (\Sigma_g))\) has a simple description and the associated bundle may be extended to a projectively flat bundle over the moduli space of principally polarized abelian varieties. As a consequence, it is obtained a family of invariants for closed oriented 3-manifolds which do coincide with those defined by Witten for lens spaces and torus bundles.
Mathematics Subject Classification ID: 58D27
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57R65
Mathematics Subject Classification ID: 14K25
Mathematics Subject Classification ID: 32G20
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 881730
zbMATH Keywords: Witten theory
zbMATH Keywords: Chern-Simons action
zbMATH Keywords: 3-manifolds
author: Louis Funar
reviewed by: Vasile Oproiu
MaRDI profile type: Publication
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full work available at URL: 0393-0440(94)00050-e
OpenAlex ID: W2075393012
description: scientific article; zbMATH DE number 881730