Algebraic and Geometric Topology 4 (2004), paper no. 40, pages 935-942.

Whitehead doubling persists

Stavros Garoufalidis

Abstract. The operation of (untwisted) Whitehead doubling trivializes the Alexander module of a knot (and consequently, all known abelian invariants), and converts knots to topologically slice ones. In this note we show that Whitehead doubling does not trivialize the rational function that equals to the 2-loop part of the Kontsevich integral.

Keywords. Whitehead double, loop filtration, Goussarov-Habiro, clovers, claspers, Kontsevich integral

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

DOI: 10.2140/agt.2004.4.935

E-print: arXiv:math.GT/0003189

Submitted: 27 March 2001. (Revised: 27 September 2004.) Accepted: 28 September 2004. Published: 13 October 2004.

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Stavros Garoufalidis
School of Mathemtaics, Georgia Institute of Technology
Atlanta, GA 30332-0160, USA.
Email: stavros@maths.gatech.edu
URL: http://www.math.gatech.edu/~stavros

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