Rewriting systems in alternating knot groups with the Dehn presentation

Fabienne Chouraqui

doi:10.1007/s10711-008-9306-5

Rewriting systems in alternating knot groups with the Dehn presentation

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

Abstract

Every tame, prime and alternating knot is equivalent to a tame, prime and alternating knot in regular position, with a common projection. In this work, we show that the Dehn presentation of the knot group of a tame, prime, alternating knot, with a regular and common projection has a finite and complete rewriting system. Although there are rules in the rewriting system with left-hand side a generator and which increase the length of the words we show that the system is terminating.

Original language	English
Pages (from-to)	173-192
Number of pages	20
Journal	Geometriae Dedicata
Volume	138
Issue number	1
DOIs	https://doi.org/10.1007/s10711-008-9306-5
State	Published - Feb 2009
Externally published	Yes

Keywords

Knot and link groups
Presentation of groups
Rewriting systems
Word problem

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s10711-008-9306-5

Cite this

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abstract = "Every tame, prime and alternating knot is equivalent to a tame, prime and alternating knot in regular position, with a common projection. In this work, we show that the Dehn presentation of the knot group of a tame, prime, alternating knot, with a regular and common projection has a finite and complete rewriting system. Although there are rules in the rewriting system with left-hand side a generator and which increase the length of the words we show that the system is terminating.",

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KW - Word problem

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Rewriting systems in alternating knot groups with the Dehn presentation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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