MathOverflow

Consider the action of $\operatorname{Out(F_2)}$ on conjugacy classes of $F(a,b)$. For brevity, let us call the stabiliser of a conjugacy class, or cyclic word, $[w]$ under this action the "outer stabiliser of $[w]$" or $\overline{\operatorname{St}}...

This may be a naive question.
Let $d$ be a positive integer and let $W=C([0,1];\mathbb{R}^d)$ denote the space of $\mathbb{R}^d$-valued continuous functions on $[0,1]$ equipped with the uniform topology. Let $\{\mu_n\}_{n=1}^\infty$ be $\sigma$-finite measures on $W$....

Let $n \geq 2$ be an integer. Assume given $n(n - 1)$ points on $\mathbb{C}P^1$, say $\psi_{ij}$, indexed by$$I_n = \{ (i, j); 1 \leq i, j \leq n \text{ and } i \neq j \}.$$We assume that $\psi_{ij} \neq \psi_{ji}$, whenever $(i, j) \in I_n$.
Note that, dually, a point on $\mathbb{C}P^1$, with homogeneous coordinates $[u:v]$, defines a nonzero complex polynomial of degree at most 1, defined up to multiplication by a nonzero complex number, given by...

Let $M \colon \{0, \dots, n\} \to \mathbb{Z}\text{-}\mathbf{Mod}$ be a persistencemodule with finitely generated stalks. At each step $i$, the structure map$\varphi_i \colon M(i) \to M(i+1)$ is a $\mathbb{Z}$-linear map between finitelygenerated abelian...