A filtration of the set of integral homological 3-spheres
type: Item
instance of: scholarly article
title: A filtration of the set of integral homological 3-spheres
zbMATH Open document ID: 0907.57012
author: Tomotada Ohtsuki
published in: Documenta Mathematica
publication date: 1998-08-06T00:00:00Z
full work available at URL: https://eudml.org/doc/224117
full work available at URL: Ohtsuki.MAN.html
review text: The author reviews the Kontsevich and Vassiliev invariants for \(3\)-manifolds and discusses a universal perturbative invariant, the LMO invariant. This invariant can be expressed as the exponential of a linear sum of connected web diagrams and is universal among perturbative and finite type invariants. Two integral homology spheres are defined to be \(d\)-equivalent if all their finite type invariants of degree \(<d\) agree. This induces a filtration on the sets of equivalence classes of \(\mathbb Z\)-homology spheres.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 1184325
zbMATH Keywords: Kontsevich invariant
zbMATH Keywords: Vassiliev invariant
zbMATH Keywords: homology spheres
zbMATH Keywords: universal invariant
zbMATH Keywords: LMO invariant
reviewed by: Wolfgang Heil
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1184325