相关论文: The extended mapping class group is generated by t…
Matrix transposition induces an involution on the isomorphism classes of semi-simple n-dimensional representations of the three string braid group. We show that a connected component of this variety can detect braid-reversion or that the…
Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…
We construct several families of embeddings of braid groups into mapping class groups of orientable and non-orientable surfaces and prove that they induce the trivial map in stable homology in the orientable case, but not so in the…
We give an infinite presentation for the mapping class group of a non-orientable surface with boundary components. The presentation is a generalization of the presentation given by the second author [15].
In this paper, we establish a bijection between the set of mutation classes of mutation-cyclic skew-symmetric integral 3x3-matrices and the set of triples of integers (a,b,c) which are all greater than 1 and where the product of the two…
In this chapter, we discuss normal generators for mapping class groups of surfaces. Especially, we focus on the relation between normal generation of a mapping class with its asymptotic translation lengths on the Teichm\"uller space and the…
We consider $u_t=u^{\alpha} u_{xxx}+n(u)u_xu_{xx}+m(u)u_x^3+ r(u)u_{xx} +p(u)u_x^2 + q(u)u_x+s(u)$ with $\alpha=0$ and $\alpha=3$, for those functional forms of $m, n, p, q, r, s$ for which the equation is integrable in the sense of an…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
The mapping class group of a surface with one boundary component admits numerous interesting representations including as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class…
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…
In this research we continue our previous investigation of wreath product normal structure \cite{SkuESL}. We generalize the group of unimodular matrices \cite{Amit} and find its structure. For this goal we propose one extension of the…
We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first charac- terize some functions having linear translators, based on which several families of…
Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
A (discrete) dynamical system may have various symmetries and reversing symmetries, which together form its so-called reversing symmetry group. We study the set of 3D trace maps (obtained from two-letter substitution rules) which preserve…
We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.
Given an action of a finite group on a triangulated category with a suitable strong exceptional collection, a construction of Elagin produces an associated strong exceptional collection on the equivariant category. We prove that the…
Let Gamma be a group generated by two positive multi-twists. We give some sufficient conditions for Gamma to be free or have no `unexpectedly reducible' elements. For a group Gamma generated by two Dehn twists, we classify the elements in…
An element of a group is \emph{reversible} if it is conjugate to its own inverse, and it is \emph{strongly reversible} if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be…
We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…