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Suppose $G = F/R$ is a finitely presented group with $F = F_n$ a free group and $R$ the normal closure of words $W_1, \dots, W_p$, not all of which are products of commutators. An obvious necessary co …

The number of conjugacy classes in $S_n$ is given by the number of partitions of $n$. Do other families of finite groups have a highly combinatorial structure to their number of conjugacy classes? For …

I'm not sure if this is exactly what you were asking about, but one way of parsing your question is to ask when a homomorphism from $G$ to $\operatorname{MCG}(M)$ is induced from a homomorphism $G \to …

After lots of trial and error, it looks like I can give an explicit construction of such a Hermitian form, although it's utterly mysterious to me where such a thing comes from! Let $e_1, \dots, e_n$ …

In a 1984 paper, Squier wrote down an explicit Hermitian form $J$ relative to which the reduced Burau representation is unitary. The form is valued in the ring $\mathbb{Z}[s^{\pm 1}]$, where $s^2 = t$ …

In 1968, Arnol'd proved that the integral cohomology of the pure braid group $P_n$ is isomorphic to the exterior algebra generated by the collection of degree-one classes $\omega_{i,j}\ (1 \le i < j \ …