We prove that the 7-strand braid group is CAT(0) by elaborating on argument of Haettel, Kielak, and Schwer.

This paper is about Braids and the Artin braid group Bn. After some initial definitions and examples, I proceed to show how the Jones polynomial can be derived through a representation of the braid group by the Temperley-Lieb Algebra, an approach similar to Jones’ original construction. 1 Braids, An Introduction Perhaps the most obvious place to start is with the definition [3] of a braid: Defi...

From the braid-valued Burau module over the braid group we construct the Yang-Baxter matrices yielding the Alexanderand the Jones knot invariants. This generalises an observation of V. F. R. Jones.

From the braid-valued Burau module over the braid group we construct the Yang-Baxter matrices yielding the Alexander-and the Jones knot invariants. This generalises an observation of V. F. R. Jones.

We show that the Steinberg group $\text{St}(C_2,{\mathbb Z})$ associated with Lie type $C_2$ and integer coefficients can be realized as a quotient of braid $B_6$ by one relation. As an application we give new braid-like presentation symplectic modular $\text{Sp}_4({\mathbb Z})$.

We investigate the cohomology of level 4 subgroup braid group, namely, kernel mod reduction Burau representation at $$t=-1$$ . This group is also equal to 2 abelianization pure group. give an exact formula for first Betti number; it a quartic polynomial in number strands. show that, like homology satisfies uniform stability sense Church and Farb. Unlike symmetries—the quotient by subgroup—is on...