Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

In complex hyperbolic geometry we consider an open set biholomorphic to an open ball in Cn, and we equip it with a particular metric that makes it have constant negative holomorphic curvature. This is analogous to but different from the real hyperbolic space. In the complex case, the sectional curvature is constant on complex lines, but it changes when we consider real 2-planes which are not complex lines.

Complex Hyperbolic Geometry

The Eisenstein-Picard modular group ${\rm PU}(2,1;\mathbb {Z}[\omega])$ is defined to be the subgroup of ${\rm PU}(2,1)$ whose entries lie in the ring $\mathbb {Z}[\omega]$, where $\omega$ is a cube root of unity. This group acts isometrically and properly discontinuously on ${\bf H}^2_\mathbb{C}$, that is, on the unit ball in $\mathbb {C}^2$ with the Bergman metric. We construct a fundamental domain for the action of ${\rm PU}(2,1;\mathbb {Z}[\omega])$ on ${\bf H}^2_\mathbb {C}$, which is a 4-simplex with one ideal vertex. As a consequence, we elicit a presentation of the group (see Theorem 5.9). This seems to be the simplest fundamental domain for a finite covolume subgroup of ${\rm PU}(2,1)$

/pdf/the-geometry-of-the-eisenstein-picard-modular-group-3h8e5e89c4.pdf

The geometry of the Eisenstein-Picard modular group

We produce a family of new, non-arithmetic lattices in $${\mathrm{PU}}(2,1)$$
 . All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne–Mostow, and fell into nine commensurability classes. Our groups produce five new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for constructing fundamental domains for discrete groups acting on the complex hyperbolic plane.

/pdf/new-non-arithmetic-complex-hyperbolic-lattices-2jfu8yll24.pdf

New non-arithmetic complex hyperbolic lattices

We show that the figure eight knot complement admits a uniformizable spherical CR structure, i.e. it occurs as the manifold at infinity of a complex hyperbolic orbifold. The uniformization is unique provided we require the peripheral subgroups to have unipotent holonomy.

https://webusers.imj-prg.fr/~elisha.falbel/figure8.pdf

Complex hyperbolic geometry of the figure eight knot

We give a new construction of fundamental domains in H C for the action of certain lattices in PU(2, 1) defined by Mostow. The polyhedra are given a natural geometric description starting from certain fixed points of elliptic elements. Among the advantages over Dirichlet domains, we gain a simplification of the combinatorics and obtain proofs using mainly synthetic arguments.

/pdf/new-constructions-of-fundamental-polyhedra-in-complex-185zv6poha.pdf

New constructions of fundamental polyhedra in complex hyperbolic space

https://www-fourier.ujf-grenoble.fr/~deraux/recherche/tg4445.pdf

Deforming the r-fuchsian (4,4,4)-triangle group into a lattice

We produce a family of new, non arithmetic lattices in PU(2,1). All previously known examples were commensurable with lattices constructed by Picard, Mostow and Deligne-Mostow, and fell into 9 commensurability classes. Our groups produce 5 new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for constructing fundamental domains for discrete group acting on the complex hyperbolic plane.

/pdf/new-non-arithmetic-complex-hyperbolic-lattices-3bxwsqpeo7.pdf

Martin Deraux

Papers

New non-arithmetic complex hyperbolic lattices

Complex hyperbolic geometry of the figure eight knot

New constructions of fundamental polyhedra in complex hyperbolic space

Deforming the r-fuchsian (4,4,4)-triangle group into a lattice

New non-arithmetic complex hyperbolic lattices