Octagon and Tropical Octagon Yield Braid Invariants

In the present paper, we construct an invariant of braids in the real projective plane which corresponds to an “action” of braids on certain graphs in ℝP 2 with labels. This paper is a sequel of papers [5],[4]. It demonstrates once more that solutions to the octagon relation in various forms give rise to invariants of braids.

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Publication Details

Journal
Journal of Knot Theory and Its Ramifications
Published
2026-10-30
DOI
https://doi.org/10.1142/s021821652640016x
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Octagon and Tropical Octagon Yield Braid Invariants

Vassily Olegovich Manturov
Journal of Knot Theory and Its Ramifications
Geometric and Algebraic Topology
article

Octagon and Tropical Octagon Yield Braid Invariants

Vassily Olegovich Manturov
article en

Abstract

In the present paper, we construct an invariant of braids in the real projective plane which corresponds to an “action” of braids on certain graphs in ℝP 2 with labels. This paper is a sequel of papers [5],[4]. It demonstrates once more that solutions to the octagon relation in various forms give rise to invariants of braids.

Journal of Knot Theory and Its Ramifications
Openalex Percentile: Top 92%
Geometric and Algebraic Topology
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Octagon and Tropical Octagon Yield Braid Invariants — Vassily Olegovich Manturov · Journal of Knot Theory and Its Ramifications (2026) | TGRS Research Map | TGRS