Tangle contact homology

Johan Asplund

doi:10.1142/S0129167X24500447

Tangle contact homology

Johan Asplund

Mathematics

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

1 Scopus citations

Abstract

Knot contact homology is an ambient isotopy invariant of knots and links in ℝ³. The purpose of this paper is to extend this definition to an ambient isotopy invariant of tangles and prove that gluing of tangles gives a gluing formula for knot contact homology. As a consequence of the gluing formula we obtain that the tangle contact homology detects triviality of tangles.

Original language	English
Article number	2450044
Journal	International Journal of Mathematics
Volume	35
Issue number	12
DOIs	https://doi.org/10.1142/S0129167X24500447
State	Published - Oct 1 2024

Keywords

Knot contact homology
tangles

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10.1142/S0129167X24500447

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title = "Tangle contact homology",

abstract = "Knot contact homology is an ambient isotopy invariant of knots and links in ℝ3. The purpose of this paper is to extend this definition to an ambient isotopy invariant of tangles and prove that gluing of tangles gives a gluing formula for knot contact homology. As a consequence of the gluing formula we obtain that the tangle contact homology detects triviality of tangles.",

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AU - Asplund, Johan

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N2 - Knot contact homology is an ambient isotopy invariant of knots and links in ℝ3. The purpose of this paper is to extend this definition to an ambient isotopy invariant of tangles and prove that gluing of tangles gives a gluing formula for knot contact homology. As a consequence of the gluing formula we obtain that the tangle contact homology detects triviality of tangles.

AB - Knot contact homology is an ambient isotopy invariant of knots and links in ℝ3. The purpose of this paper is to extend this definition to an ambient isotopy invariant of tangles and prove that gluing of tangles gives a gluing formula for knot contact homology. As a consequence of the gluing formula we obtain that the tangle contact homology detects triviality of tangles.

KW - Knot contact homology

KW - tangles

UR - https://www.scopus.com/pages/publications/85198929448

U2 - 10.1142/S0129167X24500447

DO - 10.1142/S0129167X24500447

M3 - Article

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SN - 0129-167X

VL - 35

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 12

M1 - 2450044

ER -

Tangle contact homology

Abstract

Keywords

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