Related papers: Generating the Level 2 Subgroup by Involutions
Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface of genus $g \geq 1$, and let $\mathrm{LMod}_{p}(X)$ be the liftable mapping class group associated with a finite-sheeted branched cover $p:S \to X$, where…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
Let $\rm{Mod(S)}$ be the mapping class group of a closed orientable surface $S$ of genus $g \geq 2$. Let $G$ be a non-elementary subgroup of $\rm{Mod(S)}$ so that the associated Bowen-Margulis measure is finite. In this paper, we give an…
When we consider a finite abelian group acting linearly on a polynomial ring, we can find monomial generators for the subring of invariants. By Noether's degree bound and Hilbert's finiteness theorem, we know that there are finitely many…
Let $S_g$ be the closed oriented surface of genus $g \geq 0$, and let $\mathrm{Mod}(S_g)$ be the mapping class group of $S_g$. For $g\geq 2$, we develop an algorithm to obtain a finite generating set for the liftable mapping class group…
A variational approach to the reconstruction of a shape (2D simple manifolds) as triangulated surface from given level set using shape gradients is presented. It involves an energy functional that depends on the local shape characteristics…
We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.
We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on…
We introduce geometric invariants for $p$-groups of class $2$ and exponent $p$. We report on their effectiveness in distinguishing among 5-generator $p$-groups of this type.
We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.
In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co)homology are also mentioned.
We survey recent developments on mapping class groups of surfaces of infinite topological type.
We give an algorithm to calculate the minimal and maximal genus of the orientable closed surface where a graph $G$ can be embedded. For this, we construct some special branched coverings of the 2-sphere. We apply this algorithm to calculate…
We describe separating G_2-invariants of several copies of the algebra of octonions over an algebraically closed field of characteristic two. We also obtain a minimal separating and a minimal generating set for G_2-invariants of several…
An upper bound on degrees of elements of a minimal generating system for invariants of quivers of dimension (2,...,2) is established over a field of arbitrary characteristic and its precision is estimated. The proof is based on the…
For immersed surfaces in the four-space, we have a generating set of the Swenton--Hughes--Kim--Miller spatial moves that relate singular banded diagrams of ambient isotopic immersions of those surfaces. We also have…
We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…
Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act as parametric level sets with the zero-level set defining the surface of interest. We present a…
We consider the function $f(g)$ that assigns to an orientable surface $M$ of genus $g$ the maximal number of free commuting independent involutions on $M$. We show that the surface of minimal genus $g$ with $f(g)=n$ is a real moment-angle…