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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Concordance and 1–loop clovers

Stavros Garoufalidis and Jerome Levine

Algebraic & Geometric Topology 1 (2001) 687–697

arXiv: math.GT/0102102

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
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M25
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Publication
Received: 10 July 2001
Revised: 14 November 2001
Accepted: 16 November 2001
Published: 19 November 2001
Authors
Stavros Garoufalidis
Department of Mathematics
University of Warwick
Coventry CV4 7AL
UK
Jerome Levine
Department of Mathematics
Brandeis University
Waltham MA 02254-9110
USA