Topological invariants for 3-manifolds using representations of mapping class groups. I
type: Item
instance of: scholarly article
title: Topological invariants for 3-manifolds using representations of mapping class groups. I
zbMATH Open document ID: 0762.57011
DOI: 10.1016/0040-9383(92)90016-B
author: Thoshitake Kohno
published in: Topology
publication date: 1993-01-16T00:00:00Z
review text: The author introduces new invariants of closed orientable 3-manifolds via their Heegaard decompositions. First a finite dimensional vector space is associated with the Heegaard surface \(\Sigma_ g\); the author then constructs projectively linear representations of the mapping class group of \(\Sigma_ g\) using the vector space mentioned above. This requires a considerable amount of techniques used in conformal field theory. The invariants themselves are defined by applying these representations to the gluing homeomorphism of \(\Sigma_ g\) with respect to certain distinguished bases of the vector space. Topological invariance is proved by way of Reidemeister-Singer. It is mentioned that the invariants distinguish the lens spaces \(L(7,1)\) and \(L(7,2)\), and hence are not homotopy invariants.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 89829
zbMATH Keywords: quantum group invariants of 3-manifolds
zbMATH Keywords: Witten invariants of 3- manifolds
zbMATH Keywords: Heegaard decompositions
zbMATH Keywords: projectively linear representations of the mapping class group
zbMATH Keywords: conformal field theory
reviewed by: Gerhard Burde
MaRDI profile type: Publication
full work available at URL: 0040-9383(92)90016-b
OpenAlex ID: W2089937744
description: scientific article; zbMATH DE number 89829