Concordance and 1–loop clovers

Stavros Garoufalidis; Jerome Levine

doi:10.2140/agt.2001.1.687

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Home > Journals > Algebr. Geom. Topol. > Volume 1 > Issue 2 > Article

2001 Concordance and 1–loop clovers

Stavros Garoufalidis, Jerome Levine

Algebr. Geom. Topol. 1(2): 687-697 (2001). DOI: 10.2140/agt.2001.1.687

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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.

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Stavros Garoufalidis. Jerome Levine. "Concordance and 1–loop clovers." Algebr. Geom. Topol. 1 (2) 687 - 697, 2001. https://doi.org/10.2140/agt.2001.1.687