Volume 4 (2002)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Other MSP Publications

Cubic complexes and finite type invariants

Sergei Matveev and Michael Polyak

Geometry & Topology Monographs 4 (2002) 215–233

DOI: 10.2140/gtm.2002.4.215

Abstract

Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the ‘cubic’ point of view. Finite type invariants of knots and homology 3-spheres fit perfectly into this conception. In particular, we get a natural explanation why they behave like polynomials.

Keywords

cubic complexes, finite type invariants, polynomial functions, Vassiliev invariants

Mathematical Subject Classification

Primary: 55U10, 55U99

Secondary: 13B25, 57M27

References
Publication

Received: 7 April 2002
Revised: 12 October 2002
Accepted: 10 September 2002
Published: 13 October 2002

Authors
Sergei Matveev
Department of Mathematics
Chelyabinsk State University
Chelyabinsk 454021
Russia
Michael Polyak
Department of Mathematics
Technion – Israel Institute of Technology
32000 Haifa
Israel