On the existence of finite type link homotopy invariants

Blake Mellor; Dylan Thurston

On the existence of finite type link homotopy invariants

Mathematics, Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

Abstract

We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there must exist finite type homotopy invariants which are not products of the linking numbers. This corrects previous errors of the first author.

Original language	English
Pages (from-to)	1025-1040
Journal	Journal of Knot Theory and its Ramifications
Volume	10
Issue number	7
State	Published - 2001

Disciplines

Geometry and Topology

Cite this

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title = "On the existence of finite type link homotopy invariants",

abstract = " We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there must exist finite type homotopy invariants which are not products of the linking numbers. This corrects previous errors of the first author.",

author = "Blake Mellor and Dylan Thurston",

note = "Mellor, B. and D. Thurston, 2001: On the existence of finite type link homotopy invariants. J. Knot Theory Ramif., 10.7, 1025-1040, arXiv:math/0010206.",

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AB - We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there must exist finite type homotopy invariants which are not products of the linking numbers. This corrects previous errors of the first author.

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

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On the existence of finite type link homotopy invariants

Abstract

Disciplines

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