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arxiv: 2411.18783 · v1 · pith:3BPESEKXnew · submitted 2024-11-27 · 🧮 math.GT · math.GR

Quasitoric representation of generalized braids

classification 🧮 math.GT math.GR
keywords generalizedbraidnormalquasitorictheoriesbraidsknotprove
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In this paper, we define generalized braid theories in alignment with the language of Fenn and Bartholomew for knot theories, and compute a generating set for the pure generalized braid theories. Using this, we prove that every oriented normal generalized knot is the closure of a quasitoric normal generalized braid. Further, we prove that the set of quasitoric normal generalized braids forms a subgroup of normal generalized braid group.

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