5 problems

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

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 $g\geq 2$ 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 $S_{g,n}$ be an orientable surface of genus $g$ with $n$ punctures, and let $f\in\mathrm{Mod}(S_{g,n})$ be a pseudo-Anosov mapping class, meaning that it has a representative p…

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…