Volume 5, issue 2 (2001)

Download this article
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Homology surgery and invariants of 3–manifolds

Stavros Garoufalidis and Jerome Levine

Geometry & Topology 5 (2001) 551–578

arXiv: math.GT/0005280

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.

Keywords
homology surgery, finite type invariants, 3–manifolds, clovers
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M25
References
Forward citations
Publication
Received: 31 May 2000
Revised: 2 May 2001
Published: 17 June 2001
Proposed: Robion Kirby
Seconded: Joan Birman, Cameron Gordon
Authors
Stavros Garoufalidis
School of Mathematics
Georgia Institute of Technology
Atlanta
Georgia 30332-0160
USA
Jerome Levine
Department of Mathematics
Brandeis University
Waltham
Massachusetts 02254-9110
USA