Concordance and 1-loop clovers
arXiv:math/0102102 · doi:10.2140/agt.2001.1.687
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.
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-33.abs.html
References in corpus (6)
- Claspers and finite type invariants of links
- Homology cylinders: an enlargement of the mapping class group
- Calculus of clovers and finite type invariants of 3-manifolds
- A rational noncommutative invariant of boundary links
- Covering Spaces over Claspered Knots
- Finite type invariants of knots via their Seifert matrices
Cited by in corpus (9)
- A rational noncommutative invariant of boundary links
- Characterization of Finite Type String Link Invariants of Degree < 5
- Links with trivial Alexander module and nontrivial Milnor invariants
- Strong S-equivalence of ordered links
- Abelian quotients of the string link monoid
- Grope Cobordism and Feynman Diagrams
- A surgery view of boundary links
- On Knots with trivial Alexander polynomial
- The loop expansion of the Kontsevich integral, the null move and S-equivalence