Concordance and 1–loop clovers

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.

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Keywords

concordance, $S$–equivalence, clovers, finite type invariants

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M25

References

Forward citations

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

Volume 1, issue 2 (2001)

Stavros Garoufalidis and Jerome Levine

Abstract