Related papers: A presentation of the even spin mapping class grou…
In this survey we show how well known results about the Word Problem for finite group presentations can be generalized to the Word Problem and other decision problems for non-necessarily finite monoid and group presentations. This is done…
Extended affine Weyl groups are the Weyl groups of extended affine root systems. Finite presentations for extended affine Weyl groups are known only for nullities $\leq 2$, where for nullity 2 there is only one known such presentation. We…
Finite presentations for the mapping class group M(F) are known for arbitrary orientable compact surface F. If F is non-orientable, then such presentations are known only when F has genus at most 3 and few boundary components. In this paper…
In this note, we investigate how different fundamental groups of presentations of a fixed algebra $A$ can be. For finitely many finitely presented groups $G_i$, we construct an algebra $A$ such that all $G_i$ appear as fundamental groups of…
We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algebras.
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…
For a connected graph L, let G(L) be a group with generators the vertex set of L, subject only to the relations that the ends of each edge commute. Now let H(L) be the kernel of the homomorphism from G(L) to the integers that takes each…
We introduce two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function) for infinite group presentations and prove the fundamental equivalence between the solvability of the word…
In this paper, we construct an infinite presentation of the Torelli subgroup of the mapping class group of a surface whose generators consist of the set of all "separating twists", all "bounding pair maps", and all "commutators of simply…
We give several necessary and sufficient conditions for the existence of {\it the presentation by conjugation} for a non-simply laced extended affine Weyl group. We invent a computational tool by which one can determine simply the existence…
Given any finitely presented group G we find a triangular algebra such that has two presentations, one with fundamental group G and another with trivial group. Thus proving that given a collection G1,...,Gn of finitely presented groups…
In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include…
In a previous paper, we defined a higher dimensional analog of Thompson's group V, and proved that it is simple, infinite, finitely generated, and not isomorphic to any of the known Thompson groups. There are other Thompson groups that are…
Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…
The aim of this paper is to survey some known results about mapping class group quotients by powers of Dehn twists, related to their finite dimensional representations and to state some open questions. One can construct finite quotients of…
In this note we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if $H$ is a finitely generated normal subgroup of a finitely presented group $G$ with $G/H$ cyclic, then $H$ has…
We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
Let f be a Z/2Z-spin structureon a closed surface S of genus g>3. We determine a generating set of the stabilizer of f in the mapping class group of S consisting of Dehn twists about an explicit collection of 2g+1 curves in S. If g=3 then…
We consider finite-sheeted, regular, possibly branched covering spaces of compact surfaces with boundary and the associated liftable and symmetric mapping class groups. In particular, we classify when either of these subgroups coincides…