Related papers: Dehn twists have roots
The twistor method is applied for obtaining examples of generalized Kaehler structures which are not yielded by Kaehler structures.
The Dehn quandle of a closed orientable surface is the set of isotopy classes of non-separating simple closed curves with a natural quandle structure arising from Dehn twists. In this paper, we consider finiteness of some canonical…
We generalize the idea of unknotting knots to Seifert surfaces. We define an operation called ribbon twist which serves as the equivalent of a crossing change for knots. A Seifert surface is considered untwisted, the equivalent to…
We give examples of dynamical twists in finite-dimensional Hopf algebras over an arbitrary Hopf subalgebra. The construction is based on the categorical approach of dynamical twists introduced by Donin and Mudrov.
We consider conditions on relatively hyperbolic groups about the non-existence of certain kinds of splittings, and show these properties persist in long Dehn fillings. We deduce that certain connectivity properties of the Bowditch boundary…
Let $M$ be a simple 3-manifold with a toral boundary component. It is known that if two Dehn fillings on $M$ along the boundary produce a reducible manifold and a toroidal manifold, then the distance between the filling slopes is at most…
We construct normal rationally connected varieties (of arbitrarily large dimension) not containing any smooth rational curves.
We show that on a nonorientable surface of genus at least 7 any power of a Dehn twist is equal to a single commutator in the mapping class group and the same is true, under additional assumptions, for the twist subgroup, and also for the…
Unifying various constructions of quandles including Coxeter quandles, free quandles, knot quandles of prime knots and Dehn quandles of orientable surfaces, we introduce Dehn quandles of groups with respect to their subsets. It turns out…
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…
As is well-known, the Witten deformation of the De Rham complex computes the De Rham cohomology. In this paper we study the Witten deformation on a noncompact manifold and restrict it to differential forms which behave polynomially near…
We exhibit the first examples of exotic contactomorphisms with infinite order as elements of the contact mapping class group. These are given by certain Dehn twists on the separating sphere in a connected sum of two closed contact…
Distinct knots K, K' can sometimes share a common p/q-framed Dehn surgery. A folk conjecture held that for a fixed pair of knots, this can occur for at most one value of p/q. We disprove this conjecture by constructing pairs of distinct…
This is a study of the construction of particular regular sub-n-gons T in regular n-gons P using a special system of chords of P. In particular, some of these sub-n-gons have areas which are integer divisors of the area of the given n-gon…
We consider the derivatives which appear in the context of noncommutative string theory. First, we identify the correct derivations to use when the underlying structure of the theory is a quasitriangular Hopf algebra. Then we show that this…
Let T(N) be the subgroup of the mapping class group of a nonorientable surface N (possibly with punctures and/or boundary components) generated by twists about two-sided circles. We obtain a simple generating set for T(N). As an application…
Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For…
We propose a general procedure to construct noncommutative deformations of an embedded submanifold $M$ of $\mathbb{R}^n$ determined by a set of smooth equations $f^a(x)=0$. We use the framework of Drinfel'd twist deformation of differential…
This note introduces a class of nonlinear Neumann problems on balls expanding with the radii tending towards infinity. Performing singular perturbation arguments, we establish the corresponding concentration phenomenon and refined…
The Dehn property for a complex is that every non-trivial disk diagram has spurs or shells. It implies a linear isoperimetric inequality. It has been conjectured that the same is true of a more general property which also allows cutcells.…