Related papers: Combining Rational maps and Kleinian groups via or…

The structure of Poisson polynomial algebras of the type obtained as semiclassical limits of quantized coordinate rings is investigated. Sufficient conditions for a rational Poisson action of a torus on such an algebra to leave only…

Since the end of the XIXth century, we know that each birational map of the complex projective plane is the product of a finite number of quadratic birational maps of the projective plane; this motivates our work which essentially deals…

Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by…

We study the geometry of horospheres in Teichm\"uller space of Riemann surfaces of genus g with n punctures, where $3g-3+n\geq 2$. We show that every $C^1$-diffeomorphism of Teichm\"uller space to itself that preserves horospheres is an…

We classify all torsion-free derived arithmetic Fuchsian groups of genus two by commensurability class. In particular, we show that there exist no such groups arising from quaternion algebras over number fields of degree greater than 5. We…

The notion of i-bounded geometry generalises simultaneously bounded geometry and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by…

In this article we introduce the notion of a k-almost-quasifibration and give many examples. We also show that a large class of these examples are not quasifibrations. As a consequence, supporting the Asphericity conjecture of [19], we…

A knot in a solid torus defines a map on the set of (smooth or topological) concordance classes of knots in $S^3$. This set admits a group structure, but a conjecture of Hedden suggests that satellite maps never induce interesting…

We compute the factorisation homology of the four-punctured sphere and punctured torus over the quantum group $\mathcal{U}_q(\mathfrak{sl}_2)$ explicitly as categories of equivariant modules using the framework of `Integrating Quantum…

Answering a question posed by Adam Epstein, we show that the collection of conjugacy classes of polynomials admitting a parabolic fixed point and at most one infinite critical orbit is a set of bounded height in the relevant moduli space.…

In this work, we identify a certain family of higher-dimensional formal groups over the ring of $p$-adic integers such that any two formal groups in that class coincide if they share infinitely many torsion points. As a useful application,…

A classical result in differential geometry states that for a free and proper Lie group action, the quotient map to the orbit space induces an isomorphism between the de Rham complex of differential forms on the orbit space and the basic…

This dissertation concerns the classification of groupoid and higher-rank graph C*-algebras and has two main components. Firstly, for a groupoid it is shown that the notions of strength of convergence in the orbit space and…

We compute the group of link homotopy classes of link maps of two 2-spheres into 4-space. It turns out to be free abelian, generated by geometric constructions applied to the Fenn-Rolfsen link map and detected by two self-intersection…

We propose a novel meshless method to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic…

We classify Riemannian surfaces admitting associated families in three dimensional homogeneous spaces with four-dimensional isometry groups and in a wide family of (semi-Riemannian) warped products, with an extra natural condition (namely,…

The Reeb space of a continuous map is the space of all (elements representing) connected components of preimages endowed with the quotient topology induced from the natural equivalence relation on the domain. These objects are strong tools…

We introduce the Hermitian-invariant group $\Gamma_f$ of a proper rational map $f$ between the unit ball in complex Euclidean space and a generalized ball in a space of typically higher dimension. We use properties of the groups to define…

We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so…

We construct a morphism from the equivariant Fukaya algebra of a Lagrangian brane in the zero level set of a moment map of a Hamiltonian action to the Fukaya algebra of the quotient brane. This morphism induces a map between Maurer-Cartan…