Volume 1, issue 2 (2001)

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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
Primary: 57N10
Secondary: 57M25