8 problems

Fibred Dehn twist exact sequence conjecture. Under conditions which render $a$ and $b$ well-defined, they fit into a long exact sequence

Amorós–Bogomolov–Katzarkov–Pantev conjecture. Every right-veering mapping class is a product of positive Dehn twists:

Let $F$ be a smooth manifold homeomorphic to … Let $B\subset F$ be a small $4$-ball. A boundary Dehn twist is the boundary-supported diffeomorphism of $F\setminus B$ associated wit…

Let $a_0$ and $a_4$ be curves on the closed surface $S_g$ with $d(a_0,a_4)=4$, and let $T_{a_4}$ denote the Dehn twist about $a_4$. Two curves are minimally intersecting when their…

Let $g\geq 2$ and let $b_1,\ldots,b_n$ be curves isotopic to the boundary components of the surface $\Sigma_g^n$. For positive exponents $k_1,\ldots,k_n$, consider the product … He…

Let $\Sigma$ be the surface under discussion, let $\pi$ be its fundamental group, and let $\widehat{\mathcal{M}}=\operatorname{Aut}_{\partial}(\widehat{\pi})$ be the generalized ma…

Let $S$ be the surface under discussion, let $\gamma$ be an unoriented loop on $S$, and let $t_{\gamma}$ denote the generalized Dehn twist along $\gamma$. A loop is homotopic to a…

Ozbagci–Stipsicz conjecture. For any mapping class in $\Gamma_g^n$, there is an a priori upper bound on the length of any positive factorization of that mapping class.