Whitehead doubling persists

Garoufalidis, Stavros

doi:10.2140/agt.2004.4.935

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Whitehead doubling persists

Stavros Garoufalidis

Algebraic & Geometric Topology 4 (2004) 935–942

DOI: 10.2140/agt.2004.4.935

arXiv: math.GT/0003189

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

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M25

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Publication

Received: 27 March 2001

Revised: 27 September 2004

Accepted: 28 September 2004

Published: 13 October 2004

Authors

Stavros Garoufalidis
School of Mathemtaics Georgia Institute of Technology Atlanta GA 30332-0160 USA

Volume 4, issue 2 (2004)