Geometry & Topology, Vol. 5 (2001) Paper no. 18, pages 551--578.

Homology surgery and invariants of 3-manifolds

Stavros Garoufalidis, Jerome Levine

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 \pi-algebraically-split links in 3-manifolds with fundamental group \pi . 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 \pi-decorated trivalent graphs. We also consider an associated notion of surgery equivalence of \pi-algebraically split links and prove a classification theorem using a generalization of Milnor's \mu-invariants to this class of links.

Keywords. Homology surgery, finte type invariants, 3-manifolds, clovers

AMS subject classification. Primary: 57N10. Secondary: 57M25.

DOI: 10.2140/gt.2001.5.551

E-print: arXiv:math.GT/0005280

Submitted to GT on 31 May 2000. (Revised 2 May 2001.) Paper accepted 9 June 01. Paper published 17 June 2001.

Notes on file formats

Stavros Garoufalidis, Jerome Levine
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160, USA

Department of Mathematics
Brandeis University
Waltham, MA 02254-9110, USA


GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to