Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 14, pages 215--233.

Cubic complexes and finite type invariants

Sergei Matveev, Michael Polyak

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

AMS subject classification. Primary: 55U99, 55U10. Secondary: 57M27, 13B25.

E-print: arXiv:math.GT/0204085

Submitted to GT on 7 April 2002. (Revised 12 October 2002.) Paper accepted 10 September 2002. Paper published 13 October 2002.

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Sergei Matveev, Michael Polyak
Department of mathematics, Chelyabinsk State University
Chelyabinsk, 454021, Russia
and
Department of Mathematics, Technion - Israel Institute of Technology
32000, Haifa, Israel

Email: matveev@csu.ru, polyakm@math.technion.ac.il

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