Related papers: The mapping class group and the Meyer function for…

In this article we provide a classification and description of compact Riemann surfaces admitting a triangular action of a group of order $2p^2,$ where $p$ is an odd prime number. We obtain that all such Riemann surfaces are isomorphic to…

We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically…

In this first of a series of three papers we outline an approach to classifying 4d $\mathcal{N}{=}2$ superconformal field theories at rank 2. The classification of allowed scale invariant $\mathcal{N}=2$ Coulomb branch geometries of…

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…

This paper is a study of the subgroups of the mapping class groups of Riemann surfaces, called "geometric" subgroups, corresponding to the inclusion of subsurfaces. Our analysis includes surfaces with boundary and with punctures. The…

We show that the pure mapping class group is uniformly perfect for a certain class of infinite type surfaces with noncompact boundary components. We then combine this result with recent work in the remaining cases to give a complete…

This is a paper in smooth $4$-manifold topology, inspired by the N\'{e}ron-Lang Theorem in number theory. More precisely, we prove that a smooth version $\MW(\pi)$ of Mordell-Weil group of an elliptic fibration $\pi:M\to\Pb^1$ is finitely…

Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive…

We investigate the existence of Boolean degree $d$ functions on the Grassmann graph of $k$-spaces in the vector space $\mathbb{F}_q^n$. For $d=1$ several non-existence and classification results are known, and no non-trivial examples are…

We calculate the Picard group, over the integers, of the Hilbert scheme of smooth, irreducible, non-degenerate curves of degree $d$and genus $g \geq 4$ in ${\Bbb P}^r$, in the case when $d \geq 2g+1 $ and $r \leq d-g$. We express the…

In this work, we study the asymptotic geometry of the mapping class group and Teichmueller space. We introduce tools for analyzing the geometry of `projection' maps from these spaces to curve complexes of subsurfaces; from this we obtain…

A normal subgroup of the (extended) mapping class group of a surface is said to be geometric if its automorphism group is the mapping class group. We prove that in the case of the Cantor tree surface, every normal subgroup is geometric. We…

The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metrics on this space: so-called outer metrics are metrics that…

We construct a compactification M_d of the moduli space of plane curves of degree d. We regard a plane curve C as a surface-divisor pair (P^2,C) and define M_d as a moduli space of pairs (X,D) where X is a degeneration of the plane. We show…

Let $N_{g,n}$ be a genus $g$ compact non-orientable surface with $n$ boundaries. We explain about relations on the level $d$ mapping class group $\mathcal{M}_d(N_{g,0})$ of $N_{g,0}$ and the level $d$ principal congruence subgroup…

In this paper, we adapt the differential signature construction to the equivalence problem for complex plane algebraic curves under the actions of the projective group and its subgroups. Given an action of a group $G$, a signature map…

To any metric spaces there is an associated metric profile. The rectifiability of the metric profile gives a good notion of curvature of a sub-Riemannian space. We shall say that a curvature class is the rectifiability class of the metric…

We show that the mapping class group acts properly on the space of maximal representations of the fundamental group of a closed Riemann surface into G when G = Sp(2n,R), SU(n,n), SO*(2n) or Spin(2,n).

We investigate the automorphism groups of the algebraic curves \[ \mathcal{C}_d : y^d = \varphi_d(x), \] where $\varphi_d(x)$ denotes the Chebyshev polynomial of degree $d$, defined over a field $k$ with $p:=\operatorname{char}(k) \nmid…

We derive two types of linearity conditions for mapping class groups of orientable surfaces: one for once-punctured surface, and the other for closed surface, respectively. For the once-punctured case, the condition is described in terms of…