Geometry & Topology

Homology surgery and invariants of 3–manifolds

Stavros Garoufalidis and Jerome Levine

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Abstract

We introduce a homology surgery problem in dimension 3 which has the property that the vanishing of its algebraic obstruction leads to a canonical class of π–algebraically-split links in 3–manifolds with fundamental group π. Using this class of links, we define a theory of finite type invariants of 3–manifolds in such a way that invariants of degree 0 are precisely those of conventional algebraic topology and surgery theory. When finite type invariants are reformulated in terms of clovers, we deduce upper bounds for the number of invariants in terms of π–decorated trivalent graphs. We also consider an associated notion of surgery equivalence of π–algebraically split links and prove a classification theorem using a generalization of Milnor’s μ̄–invariants to this class of links.

Article information

Source
Geom. Topol., Volume 5, Number 2 (2001), 551-578.

Dates
Received: 31 May 2000
Revised: 2 May 2001
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513883037

Digital Object Identifier
doi:10.2140/gt.2001.5.551

Mathematical Reviews number (MathSciNet)
MR1833753

Zentralblatt MATH identifier
1009.57022

Subjects
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
homology surgery finite type invariants 3–manifolds clovers

Citation

Garoufalidis, Stavros; Levine, Jerome. Homology surgery and invariants of 3–manifolds. Geom. Topol. 5 (2001), no. 2, 551--578. doi:10.2140/gt.2001.5.551. https://projecteuclid.org/euclid.gt/1513883037


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