Related papers: On Torelli groups and Dehn twists of smooth 4-mani…

We prove that the boundary Dehn twist on $K3\#K3\setminus B^4$ is nontrivial in the smooth mapping class group, providing another example of an exotic diffeomorphism on a simply-connected spin four-manifold. We do so by finding an algebraic…

By the work of Baraglia-Konno and Kronheimer-Mrowka, the boundary Dehn twist on punctured $K3$ surfaces is nontrivial in the smooth mapping class group relative to boundary. In this short note, we prove that it becomes trivial after…

For $X$ any complete intersection of even complex dimension or any connected sum thereof (or, more generally, any space among certain broad classes of smooth manifolds), we concretely construct diffeomorphisms $a,c$ of punctured $X$ rel…

We compute the topological mapping class group of every compact, simply connected, topological 4-manifold. This was previously only known in the closed case. If the 4-manifold is smooth, we deduce an analogous description of the stable…

We consider the question of extending a smooth homotopy coherent finite cyclic group action on the boundary of a smooth 4-manifold to its interior. As a result, we prove that Dehn twists along any Seifert homology sphere, except the…

Dehn twists around simple closed curves in oriented surfaces satisfy the braid relations. This gives rise to a group theoretic from the braid group to the mapping class group. We prove here that this map is trivial in stable homology with…

By Torelli topology the author understands aspects of the topology of surfaces (potentially) relevant to the study of Torelli groups. The present paper is devoted to a new approach to the results of W. Vautaw about Dehn multi-twists in…

We prove that, for a closed oriented smooth spin 4-manifold $X$ with non-zero signature, the Dehn twist about a $(+2)$- or $(-2)$-sphere in $X$ is not homotopic to any finite order diffeomorphism. In particular, we negatively answer the…

Kronheimer-Mrowka shows that the Dehn twist along a $3$-sphere in the neck of two $K3$ surfaces is not smoothly isotopic to the identity. Their result requires that the manifolds are simply connected and the signature of one of them is $16…

For any unoriented loop on a compact connected oriented surface with one boundary component, the generalized Dehn twist along the loop is defined as an automorphism of the completed group ring of the fundamental group of the surface. If the…

We calculate the Dehn twist action on the spaces of conformal blocks of a not necessarily semisimple modular category. In particular, we give the order of the Dehn twists under the mapping class group representations of closed surfaces. For…

This article grew out of an effort to understand the smooth mapping class groups of certain 4-manifolds in a geometric manner. We prove a smooth analog of the Birman-Hilden theorem for manifolds that admit a hyperk\"ahler structure. This…

Ruberman gave the first examples of self-diffeomorphisms of four-manifolds that are isotopic to the identity in the topological category but not smoothly so. We give another example of this phenomenon, using the Dehn twist along a 3-sphere…

Positive Dehn twist products for some elements of finite order in the mapping class group of a 2-dimensional closed, compact, oriented surface $\Sigma_g$, which are rotations of $\Sigma_g$ through $2\pi /p$, are presented. The homeomorphism…

Given two Lagrangian spheres in an exact symplectic manifold, we find conditions under which the Dehn twists about them generate a free non-abelian subgroup of the symplectic mapping class group. This extends a result of Ishida for Riemann…

We provide some language for algebraic study of the mapping class groups for surfaces with non-connected boundary. As applications, we generalize our previous results on Dehn twists to any compact connected oriented surfaces with non-empty…

For each integer $n$ we construct a simply connected $4$-manifold $X$ admitting a smoothly embedded surface $\Sigma$ of self intersection number $n$ such that the complement of the surface has non-trivial fundamental group. This answers a…

We give a finite presentation of the mapping class group of an oriented (possibly bounded) surface of genus greater or equal than 1, considering Dehn twists on a very simple set of curves.

One way to better understand the smooth mapping class group of the 4-sphere would be to give a list of generators in the form of explicit diffeomorphisms supported in neighborhoods of submanifolds, in analogy with Dehn twists on surfaces.…

We prove that there exists no a priori bound on the Euler characteristic of a closed symplectic 4-manifold coming solely from the genus of a compatible Lefschetz pencil on it, nor is there a similar bound for Stein fillings of a contact…