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Publikováno v: Transactions of the American Mathematical Society.

The aim of this article is to study the SL 2 ⁡ ( C ) \operatorname {SL}_2(\mathbb {C}) –character scheme of a finitely generated group. Given a presentation of a finitely generated group Γ \Gamma , we give equations defining the coordinate ring

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d43b3004eaf75b8b1aafaece19c27079
https://doi.org/10.1090/tran/8910

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Cone 3-Manifolds

Autor: Joan Porti

Publikováno v: In the Tradition of Thurston II ISBN: 9783030975593

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f7e678d4cd26af831ad38e8466bb2737
https://doi.org/10.1007/978-3-030-97560-9_4

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Examples of character varieties in characteristic 𝑝 and ramification

Autor: Luisa Paoluzzi, Joan Porti

Publikováno v: Characters in Low-Dimensional Topology. :229-261

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a081df7e9f719e57e3434bb4d88d9518
https://doi.org/10.1090/conm/760/15294

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Character varieties and knot symmetries

Autor: Joan Porti

Publikováno v: Winter Braids Lecture Notes. 4:1-21

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::72c1558acd603e6deb06c279079af597
https://doi.org/10.5802/wbln.18

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Projective structures on a hyperbolic 3-orbifold

Autor: Stephan Tillmann, Joan Porti

Publikováno v: Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

We compute and analyse the moduli space of those real projective structures on a hyperbolic 3-orbifold that are modelled on a single ideal tetrahedron in projective space. Parameterisations are given in terms of classical invariants, traces, and geom

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::67c66dca3e6de32bef9f91dbef92d0b2
http://arxiv.org/abs/2004.06242

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Volumes of SLn(ℂ)–representations of hyperbolic 3–manifolds

Autor: Wolfgang Pitsch, Joan Porti

Publikováno v: Geometry & Topology. 22:4067-4112

Let M be a compact oriented three-manifold whose interior is hyperbolic of finite volume. We prove a variation formula for the volume on the variety of representations of π 1 ( M ) in SL n ( ℂ ) . Our proof follows the strategy of Reznikov’s rig

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::305ea7e9859afc2f3ee99cf5190a03b5
https://doi.org/10.2140/gt.2018.22.4067

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Hyperbolic polygons of minimal perimeter in punctured discs

Autor: Joan Porti

Publikováno v: Scopus-Elsevier

We prove that, among the polygons in a punctured disc with fixed angles, the perimeter is minimized by the polygon with an inscribed horocycle centered at the puncture. We generalize this to a disc with a cone point and to an annulus with a geodesic

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aefe850c807b204f00c6056651ea6fc4
https://doi.org/10.2422/2036-2145.201609_017

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Dynamics on flag manifolds: domains of proper discontinuity and cocompactness

Autor: Bernhard Leeb, Joan Porti, Michael Kapovich

Publikováno v: Kapovich, Michael; Leeb, Bernhard; & Porti, Joan. (2013). Dynamics on flag manifolds: domains of proper discontinuity and cocompactness. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/5p7628cz
Geometry & Topology
Kapovich, M; Leeb, B; & Porti, J. (2018). Dynamics on flag manifolds: Domains of proper discontinuity and cocompactness. Geometry and Topology, 22(1), 157-234. doi: 10.2140/gt.2018.22.157. UC Davis: Retrieved from: http://www.escholarship.org/uc/item/79b5x84m
Geom. Topol. 22, no. 1 (2018), 157-234

For noncompact semisimple Lie groups $G$ we study the dynamics of the actions of their discrete subgroups $\Gamma
Comment: 65 pages

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::27252217f68b3b8d5e03e5a903f2aba7
https://doi.org/10.2140/gt.2018.22.157

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Invariant character varieties of hyperbolic knots with symmetries

Autor: Joan Porti, Luisa Paoluzzi

Publikováno v: Mathematical Proceedings
Mathematical Proceedings, Cambridge University Press (CUP), 2018, 165 (2), pp.193-208. ⟨10.1017/S0305004117000391⟩
Mathematical Proceedings of the Cambridge Philosophical Society
Mathematical Proceedings of the Cambridge Philosophical Society, 2018, 165 (2), pp.193-208. ⟨10.1017/S0305004117000391⟩

We study character varieties of symmetric knots and their reductions modp. We observe that the varieties present a different behaviour according to whether the knots admit a free or periodic symmetry.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bdbde66e1a864b15de41172c2a3b34ee
https://doi.org/10.1017/s0305004117000391

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Holomorphic volume forms on representation varieties of surfaces with boundary

Autor: Michael Heusener, Joan Porti

Publikováno v: Annales Henri Lebesgue
Annales Henri Lebesgue, 2020, 3, pp.341-380. ⟨10.5802/ahl.35⟩
ahl.centre-mersenne.org/item/AHL_2020__3__341_0/
Annales Henri Lebesgue, UFR de Mathématiques-IRMAR, 2020, 3, pp.341-380. ⟨10.5802/ahl.35⟩
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the other one is t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::489ddcf5af7f3a09c299af4fb5428470
https://hal.science/hal-01770366

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