Related papers: On the order of Dehn twists

This work presents higher order Lagrangian dynamics possessing locally conformal character. More concretely, locally conformal higher order Euler-Lagrange equations are written with particular focus on the second- and the third-order cases.

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.

In this note we prove: {\it Let $D$ be a 2-strong digraph of order $n$ such that its $n-1$ vertices have degrees at least $n+k$ and the remaining vertex $z$ has degree at least $n-k-4$, where $k$ is a positive integer. If $D$ contains a…

In this note some properties of the sum of element orders of a finite abelian group are studied.

We classify all the exceptional Dehn surgeries on the minimally twisted chain links with six and seven components.

This is a survey about recent progress in Rankin-Cohen deformations. We explain a connection between Rankin-Cohen brackets and higher order Hankel forms.

We show that the $X$-torsion order of a knot, which is defined in terms of a generalised Lee complex, can be calculated using the reduced Bar-Natan--Lee--Turner spectral sequence. We use this for extensive calculations, including an example…

An upward planar order on an acyclic directed graph $G$ is a special linear extension of the edge poset of $G$ that satisfies the nesting condition. This order was introduced to combinatorially characterize upward plane graphs and…

A class of highly symmetric Markov-Dyck shifts is introduced. Topological entropies and zeta functions are determined.

We give sufficient conditions for left- and bi-orderability of fundamental groups of Ore categories in terms of indirect factors, including Thompson groups and many of their generalizations. Besides recovering known results, we prove that…

I show that one can explicitly construct topologically/geometrically distinguishable data which provide isomorphic copies (i.e. \emph{isomorphs}) of the tempered fundamental group of a geometrically connected, smooth, quasi-projective…

The notion of a complex tangent arises for embeddings of real manifolds into complex spaces. It is of particular interest when studying embeddings of real $n$-dimensional manifolds into $\mathbb{C}^n$. The generic topological structure of…

Higher twisted $K$-theory is an extension of twisted $K$-theory introduced by Ulrich Pennig which captures all of the homotopy-theoretic twists of topological $K$-theory in a geometric way. We give an overview of his formulation and key…

This is a survey on the state-of-the-art of the classification of finite-dimensional complex Hopf algebras. This general question is addressed through the consideration of different classes of such Hopf algebras. Pointed Hopf algebras…

We study deformations of the discrete Heisenberg group acting properly discontinuously on the Heisenberg group from the left and right and obtain a complete description of the deformation space.

A remarkable orbital quadrupole magnetic resonance, so-called twist mode, is predicted in alkali metal clusters where it is represented by $I^{\pi}=2^-$ low-energy excitations of valence electrons with strong M2 transitions to the ground…

We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptolemy diagrams which already appeared in our earlier work on…

Topological full groups originated from the theory of topological dynamical systems and have been having considerable impact on group theory in recent years. This text represents an introduction/survey on topological full groups. After…

Given a finite simplicial complex, a unimodular representation of its fundamental group and a closed twisted cochain of odd degree, we define a twisted version of the Reidemeister torsion, extending a previous definition of V. Mathai and S.…

We count the number of isomorphism classes of degree $d$-twists of some polarized abelian varieties over finite fields of odd prime dimension. This can be seen as a higher dimensional analogue of the counting problem for elliptic curves…