Výsledky vyhledávání - "Martin Deraux"

Torsion in 1-cusped Picard modular groups

Autor: Martin Deraux, Mengmeng Xu

Publikováno v: Transformation Groups
Transformation Groups, In press, ⟨10.1007/s00031-022-09783-z⟩

We present a systematic effective method to construct coarse fundamental domains for the action of the Picard modular groups $PU(2,1,\mathcal{O}_d)$ where $\mathcal{O}_d$ has class number one, i.e. $d=1,2,3,7,11,19,43,67,163$. The computations can be

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New Nonarithmetic Complex Hyperbolic Lattices II

Autor: Julien Paupert, John R. Parker, Martin Deraux

Publikováno v: Michigan Mathematical Journal
Michigan Mathematical Journal, University of Michigan, 2021, 70 (1), ⟨10.1307/mmj/1592532044⟩
Michigan mathematical journal, 2021, Vol.70(1), pp.133-205 [Peer Reviewed Journal]

We describe a general procedure to produce fundamental domains for complex hyperbolic triangle groups. This allows us to produce new nonarithmetic lattices, bringing the number of known nonarithmetic commensurability classes in PU(2,1) to 22.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9b4c45d5aaa09738d4e1b90a1a36a204
https://doi.org/10.1307/mmj/1592532044

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A new nonarithmetic lattice in PU(3,1)

Autor: Martin Deraux

Publikováno v: Algebraic and Geometric Topology
Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2020, 20 (2), pp.925-963. ⟨10.2140/agt.2020.20.925⟩
Algebr. Geom. Topol. 20, no. 2 (2020), 925-963

We study the arithmeticity of the Couwenberg-Heckman-Looijenga lattices in PU(n,1), and show that they contain a non-arithmetic lattice in PU(3,1) which is not commensurable to the non-arithmetic Deligne-Mostow lattice in PU(3,1).

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ce9038b79d2d0ce5c26fa9177fb7630
https://hal.archives-ouvertes.fr/hal-02965313

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Volumes of 3-ball quotients as intersection numbers

Autor: Martin Deraux

Publikováno v: Transactions of the American Mathematical Society
Transactions of the American Mathematical Society, American Mathematical Society, 2020, 373 (1), pp.343-383. ⟨10.1090/tran/7925⟩

We give an explicit description of the 3-ball quotients constructed by Couwenberg-Heckman-Looijenga, and deduce the value of their orbifold Euler characteristics. For each lattice, we also give a presentation in terms of generators and relations.

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https://hal.archives-ouvertes.fr/hal-02965312

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Non-arithmetic lattices and the Klein quartic

Autor: Martin Deraux

Publikováno v: Journal für die reine und angewandte Mathematik
Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2017, ⟨10.1515/crelle-2017-0005⟩

We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphi

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https://doi.org/10.1515/crelle-2017-0005

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Non-arithmetic ball quotients from a configuration of elliptic curves in an Abelian surface

Autor: Martin Deraux

Publikováno v: Commentarii Mathematici Helvetici
Commentarii Mathematici Helvetici, European Mathematical Society, 2018, 93 (3), pp.533-554. ⟨10.4171/CMH/443⟩

We construct some non-arithmetic ball quotients as branched covers of a quotient of an Abelian surface by a finite group, and compare them with lattices that previously appear in the literature. This gives an alternative construction, which is indepe

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https://hal.archives-ouvertes.fr/hal-01890761

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On Spherical CR Uniformization of 3-Manifolds

Autor: Martin Deraux

Publikováno v: Experimental Mathematics
Experimental Mathematics, Taylor & Francis, 2015, 24 (3), pp 355-370. ⟨10.1080/10586458.2014.996835⟩

We consider the discrete representations of 3-manifold groups into $PU(2,1)$ that appear in the Falbel-Koseleff-Rouillier census, such that the peripheral subgroups have cyclic unipotent holonomy. We show that two of these representations have conjug

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5ba6aa7b535924b9c48f72f2f384ad06
https://doi.org/10.1080/10586458.2014.996835

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New non-arithmetic complex hyperbolic lattices

Autor: Julien Paupert, Martin Deraux, John R. Parker

Publikováno v: Inventiones mathematicae, 2016, Vol.203(3), pp.681-771 [Peer Reviewed Journal]
Inventiones Mathematicae
Inventiones Mathematicae, Springer Verlag, 2016, 203 (3), pp 681-771. ⟨10.1007/s00222-015-0600-1⟩

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 group

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::694db74741acc231a2e7fad6291d5c39
http://dro.dur.ac.uk/15424/

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A 1-parameter family of spherical CR uniformizations of the figure eight knot complement

Autor: Martin Deraux

Publikováno v: Geometry and Topology
Geometry and Topology, Mathematical Sciences Publishers, 2016, 20 (6), pp.3571-3621
Geom. Topol. 20, no. 6 (2016), 3571-3621

We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small deformations of that holonomy group (such that the boundary holonomy remai

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b7ac9b0cebe4b44147156fc2efee2901
https://hal.archives-ouvertes.fr/hal-01071444/file/deformFig8.pdf

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Complex hyperbolic geometry of the figure eight knot

Autor: Elisha Falbel, Martin Deraux

Publikováno v: Geometry and Topology
Geometry and Topology, Mathematical Sciences Publishers, 2015, 19, pp.237-293. ⟨10.2140/gt.2015.19.237⟩
Geometry and Topology, 2015, 19, pp.237-293. ⟨10.2140/gt.2015.19.237⟩
Geom. Topol. 19, no. 1 (2015), 237-293

International audience; 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 per

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5d53105faadcc9c6576653622738d794
https://hal.archives-ouvertes.fr/hal-00805427v2/document

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