Related papers: Dehn twists have roots

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…

By introducing an invariant of loops on a compact oriented surface with one boundary component, we give an explicit formula for the action of Dehn twists on the completed group ring of the fundamental group of the surface. This invariant…

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…

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 note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of (0,-2)-curves on threefolds, or…

We initiate the study of exotic Dehn twists along 3-manifolds $\neq S^3$ inside $4$-manifolds, which produces the first known examples of exotic diffeomorphisms of contractible 4-manifolds, more generally of definite 4-manifolds, and exotic…

We give a parity condition of a Heegaard diagram to show that it is unstabilized. This improves the result of [5]. As an application, we construct unstabilized Heegaard splittings by Dehn twists on any given Heegaard splitting.

The nontrivial subspaces with primitive coproducts are found in the deformed universal enveloping algebras. They can form carrier spaces for additional Jordanian twists. The latter can be used to construct sequences of twists for algebras…

We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.

We prove that a variety of examples of minimal complex surfaces admit exotic diffeomorphisms, providing the first known instances of exotic diffeomorphisms of irreducible 4-manifolds. We also give sufficient conditions for the boundary Dehn…

A homeomorphism of a 3-manifold M is said to be Dehn twists on the boundary when its restriction to the boundary of M is isotopic to the identity on the complement of a collection of disjoint simple closed curves in the boundary of M. In…

We discuss how the fractional Dehn twist coefficient behaves under a fully ramified branched covering of an open book, and give applications to both topological and contact 3-manifolds. Among them, we show that non-right-veering closed…

We show that for any periodic mapping class, there is some power which maps a nonseparating, simple closed curve to a distinct, disjoint nonseparating curve. As an application of this result, we introduce the notion of stable specific…

This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of $S^4$. Secondly, we give an alternative proof of a consequence of work of Saeki, namely that…

In this paper we explicitly compute equations for the twists of all the smooth plane quartic curves defined over a number field k. Since the plane quartic curves are non-hyperelliptic curves of genus 3 we can apply the method developed by…

We study Dehn twists in the outer automorphism group of a finitely generated non-abelian free group. Our main result states that, under certain compatibility conditions, sufficiently large powers of finitely many Dehn twists generate a…

Let $N_g$ be the non-orientable surface with genus $g$, $\text{MCG}(N_g)$ be the mapping class group of $N_g$, $\mathcal{T}(N_g)$ be the index 2 subgroup generated by all Dehn twists of $\text{MCG}(N_g)$. We prove that for odd genus,…

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…

This note records the order of a higher dimensional Dehn twist in a range of topologically significant groups.

Consider cotangent bundles of exotic spheres, with their canonical symplectic structure. They admit automorphisms which preserve the part at infinity of one fibre, and which are analogous to the square of a Dehn twist. Pursuing that…