Related papers: A big mapping class acting parabolically on the no…

The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is…

We classify all negatively curved $\R^n \rtimes \R$ up to quasiisometry. We show that all quasiisometries between such manifolds (except when they are biLipschitz to the real hyperbolic spaces) are almost similarities. We prove these…

We give completely combinatorial proofs of the main results of [3] using polygons. Namely, we prove that the mapping class group of a surface with boundary acts faithfully on a finitely-generated linear category. Along the way we prove some…

We prove that, except in certain low-complexity cases, the automorphism group of the graph of pants decompositions of a nonorientable surface is isomorphic to the mapping class group of that surface.

We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problems are suggested.

We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the…

We study the action of the mapping class group M(F) on the complex of curves of a non-orientable surface F. We obtain, by using a result of K. S. Brown, a presentation for M(F) defined in terms of the mapping class groups of the…

In this work we compute the first integral cohomology of the pure mapping class group of a non-orientable surface of infinite topological type and genus at least 3. To this purpose, we also prove several other results already known for…

The fine curve graph of a surface was introduced by Bowden, Hensel, and Webb as a graph consisting of essential simple closed curves on the surface. Long, Margalit, Pham, Verberne, and Yao proved that the automorphism group of the fine…

Let $\phi:\mathcal{C}(S)\to\mathcal{C}(S')$ be a simplicial isomorphism between the curve graphs of two infinite-type surfaces. In this paper we show that in this situation $S$ and $S'$ are homeomorphic and $\phi$ is induced by a…

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].

We prove that for any infinite-type orientable surface S there exists a collection of essential curves {\Gamma} in S such that any homeomorphism that preserves the isotopy classes of the elements of {\Gamma} is isotopic to the identity. The…

We define a graph structure associated in a natural way to finite fields that nevertheless distinguishes between different models of isomorphic fields.

We show that for any surface of genus at least 3 equipped with any choice of framing, the graph of non-separating curves with winding number 0 with respect to the framing is hierarchically hyperbolic but not Gromov hyperbolic. We also…

Let $\Sigma$ be a compact, orientable surface of genus $g$, and let $\Gamma$ be a relation on $\pi_0(\partial \Sigma)$ such that the prescribed arc graph $\mathcal{A}(\Sigma,\Gamma)$ is Gromov-hyperbolic and non-trivial. We show that…

We investigate Cayley graphs of graph products by showing that graph products with vertex groups that have isomorphic Cayley graphs yield isomorphic Cayley graphs.

In this note we prove an effective characterization of when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of which curves have simple elevations, weakening the…

We consider the class of quasiprojective varieties admitting a dominant morphism onto a curve with negative Euler characteristic. The existence of such a morphism is a property of the fundamental group. We show that for a variety in this…

A rigid isotopy of real algebraic curves of a certain class is a path in the space of curves of this class. The paper's study completes the rigid isotopic classification of nonsingular real algebraic curves of bidegree (4,3) on a…

This paper completely determines the non-amenability of the mapping class groups of infinite-type surfaces, the mapping class groups of locally finite infinite graphs of higher ranks, gives an example of non-amenable stabiliser of a point…