Related papers: Groups Generated by Powers of Dehn Twists

Margalit and Schleimer constructed nontrivial roots of the Dehn twist about a nonseparating curve. We prove that the conjugacy classes of roots of the Dehn twist about a nonseparating curve correspond to the conjugacy classes of periodic…

We show that for any $n\geq 2$, two elements selected uniformly at random from a \emph{symmetrized} Euclidean ball of radius $X$ in $\textrm{SL}_n(\mathbb Z)$ will generate a thin free group with probability tending to $1$ as $X\rightarrow…

Howie and Duncan observed that a word in a free product with length at least two and which is not a proper power can be decomposed as a product of two cyclic subwords each of which is uniquely positioned. Using this property, they proved…

We consider a specific dynamical system of groups formation. It is based simultaneously on a gradient competition between groups and a strong accumulation inside groups. Such a dynamical system demonstrates interesting behavior of densities…

Necessary and sufficient conditions for finite semihypergroups to be built from groups of the same order are established

We show that for each positive integer $k$ there exist right-angled Artin groups containing free-by-cyclic subgroups whose monodromy automorphisms grow as $n^k$. As a consequence we produce examples of right-angled Artin groups containing…

In this paper we consider a group generated by two unipotent parabolic elements of ${\rm SU}(2,1)$ with distinct fixed points. We give several conditions that guarantee the group is discrete and free. We also give a result on the diameter…

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.

A gyrogroup is a structure constituting from a non-empty set and a binary operation such that satisfying the left identity, and left inverse conditions, and also has the associative-like law said to be left gyroassociativity and left loop…

We define a cell complex with an action of the even spin mapping class group, and use it to obtain a finite presentation. We also obtain a finite presentation with Dehn twist generators.

We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.

We classify the module categories over the double (possibly twisted) of a finite group.

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 survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…

We construct examples of finitely presented simple groups whose Dehn functions are at least exponential. To the best of our knowledge, these are the first such examples known. Our examples arise from R\"over-Nekrashevych groups, using…

We prove that two angle-compatible Coxeter generating sets of a given finitely generated Coxeter group are conjugate provided one of them does not admit any elementary twist. This confirms a basic case of a general conjecture which…

We construct automata over a binary alphabet with $2n$ states, $n\geq 2$, whose states freely generate a free group of rank $2n$. Combined with previous work, this shows that a free group of every finite rank can be generated by finite…

The paper gives two approaches to write explicit presentations for the class of Dehn quandles using presentations of their underlying groups. The first approach gives finite presentations for Dehn quandles of a class of Garside groups and…

Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding…

In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular,…