Algebraic and Geometric Topology 1 (2001), paper no. 33, pages 687-697.

Concordance and 1-loop clovers

Stavros Garoufalidis, Jerome Levine

Abstract. We show that surgery on a connected clover (or clasper) with at least one loop preserves the concordance class of a knot. Surgery on a slightly more special class of clovers preserves invertible concordance. We also show that the converse is false. Similar results hold for clovers with at least two loops vs. S-equivalence.

Keywords. Concordance, S-equivalence, clovers, finite type invariants

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

DOI: 10.2140/agt.2001.1.687

E-print: arXiv:math.GT/0102102

Submitted: 10 July 2001. (Revised: 14 November 2001.) Accepted: 16 November 2001. Published: 19 November 2001.

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Stavros Garoufalidis, Jerome Levine
Department of Mathematics, University of Warwick
Coventry, CV4 7AL, UK
and
Department of Mathematics, Brandeis University
Waltham, MA 02254-9110, USA

Email: stavros@maths.warwick.ac.uk, levine@brandeis.edu
URL: http://www.math.gatech.edu/~stavros, http://www.math.brandeis.edu/Faculty/jlevine/
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