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- W3105366953 abstract "We introduce the concept of `claspers,' which are surfaces in 3-manifolds with some additional structure on which surgery operations can be performed. Using claspers we define for each positive integer k an equivalence relation on links called `C_k-equivalence,' which is generated by surgery operations of a certain kind called `C_k-moves'. We prove that two knots in the 3-sphere are C_{k+1}-equivalent if and only if they have equal values of Vassiliev-Goussarov invariants of type k with values in any abelian groups. This result gives a characterization in terms of surgery operations of the informations that can be carried by Vassiliev-Goussarov invariants. In the last section we also describe outlines of some applications of claspers to other fields in 3-dimensional topology." @default.
- W3105366953 created "2020-11-23" @default.
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- W3105366953 date "2000-01-28" @default.
- W3105366953 modified "2023-10-17" @default.
- W3105366953 title "Claspers and finite type invariants of links" @default.
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- W3105366953 doi "https://doi.org/10.2140/gt.2000.4.1" @default.
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