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Invariants of 3-manifolds derived from covering presentations

Published online by Cambridge University Press:  10 May 2010

ERI HATAKENAKA
ERI HATAKENAKA*
Affiliation:
Department of Mathematics, Tokyo University of Agriculture and Technology, Naka, Koganei, Tokyo 184-8588, Japan e-mail: hataken@cc.tuat.ac.jp
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Abstract

By a covering presentation of a 3-manifold, we mean a labelled link (i.e., a link with a monodromy representation), which presents the 3-manifold as the simple 4-fold covering space of the 3-sphere branched along the link with the given monodromy. It is known that two labelled links present a homeomorphic 3-manifold if and only if they are related by a finite sequence of some local moves. This paper presents a method for constructing topological invariants of 3-manifolds based on their covering presentations. The proof of the topological invariance is shown by verifying the invariance under the local moves. As an example of such invariants, we present the Dijkgraaf–Witten invariant of 3-manifolds.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 2 , September 2010 , pp. 263 - 295
Copyright
Copyright © Cambridge Philosophical Society 2010

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