Knots and links in 2-complexes

In this paper, we introduce and study knots and links in two-dimensional complexes. In particular, we define linking numbers for oriented two-component links in 2-complexes and a Kauffman-type bracket polynomial for links in 2-complexes. We also discuss relationships with knots and links in 3-manifolds.

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Publication Details

Journal
Journal of Knot Theory and Its Ramifications
Published
2025-02-15
DOI
https://doi.org/10.1142/s0218216525400085
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Knots and links in 2-complexes

Vladimir Turaev
Journal of Knot Theory and Its Ramifications
Geometric and Algebraic Topology
article

Knots and links in 2-complexes

Vladimir Turaev
article en

Abstract

In this paper, we introduce and study knots and links in two-dimensional complexes. In particular, we define linking numbers for oriented two-component links in 2-complexes and a Kauffman-type bracket polynomial for links in 2-complexes. We also discuss relationships with knots and links in 3-manifolds.

Journal of Knot Theory and Its RamificationsVol. 34(14)
Indiana University Bloomington (US)
Openalex Percentile: Top 94%
Geometric and Algebraic Topology
DOISourceOpenAlex
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Knots and links in 2-complexes — Vladimir Turaev · Journal of Knot Theory and Its Ramifications (2025) | TGRS Research Map | TGRS