Joan Porti

Preprints

Except for the oldest ones, there is an arXiv version of my papers here.

Publications

with Michael Kapovich and Bernhard Leeb. Morse actions of discrete groups on symmetric spaces: local-to-global principle. Geometry and Topology 29:5 (2025) 2343--2390. DOI:10.2140/gt.2025.29.2343 Open access (S2O).
Deforming reducible representations of surface and 2-orbifold groups. Geometriae Dedicata 219, 54 (2025). DOI:10.1007/s10711-025-01011-8. Open access. Arxiv version: 2309.00282
with Juan Luis Durán Batalla, The deformation space of nonorientable hyperbolic 3–manifolds. Algebraic and Geometric Topology 24 (2024), no. 1, pp. 109–140. DOI:10.2140/agt.2024.24.109. Open access (S2O).
with Seokbeom Yoon, The adjoint Reidemeister torsion for the connecetd sum of knots. Quantum Topology 14 (2023), no. 3, pp. 407–428. DOI:10.4171/QT/180. Arxiv version: 2104.08150
with M. Heusener, The scheme of characters in SL2. Trans. Amer. Math. Soc. 376 (2023), 6283-6313. DOI:10.1090/tran/8910. Arxiv version: 2210.13888
with Teresa García. Actions on products of CAT(−1) spaces . Geometriae Dedicata, 217, 69 (2023). DOI: 10.1007/s10711-023-00805-y" . Arxiv version: 1809.08189
Dimension of representation and character varieties for two- and three-orbifolds . Algebraic and Geometric Topology, 22 (2022), no. 4, 1906--1967. DOI: 10.2140/agt.2022.22.1905. Arxiv version: 2009.03124
with L. Bénard, J. Dubois, and M. Heusener, Asymptotics of twisted Alexander polynomials and hyperbolic volume . Indiana Univ. Math. J., 71 (2022), no. 3, 1155–1207. DOI:10.1512/iumj.2022.71.8937. Arxiv version: 1912.12946
with S. Tillmann. Projective Structures on a Hyperbolic 3-orbifold . Acta Mathematica Vietnamica, 46(2), 347-355 (2021). DOI:10.1007/s40306-021-00419-0. Arxiv version: 2004.06242
with L. Paoluzzi. Examples of character varieties in characteristic p and ramification . Characters in low-dimensional topology, 229–261, Contemp. Math., 760, Amer. Math. Soc., Providence, RI, 2020. DOI:10.1090/conm/760/15294 Arxiv version: 1905.07196
with M. Heusener Holomorphic volume forms on representation varieties of surfaces with boundary , Annales Henri Lebesgue 3 (2020), 341-380.
with Wolfgang Pitsch. Volumes of SL(n,C)-representations of hyperbolic 3-manifolds , Geometry and Topology 22:7 (2018) 4067--4112 DOI:10.2140/gt.2018.22.4067 Arxiv version: 1704.01321
with Michael Kapovich and Bernhard Leeb. A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings , Geometry and Topology 22:7 (2018) 3827--3923 DOI:10.2140/gt.2018.22.3827 Arxiv version: 1411.4176
with Michael Kapovich and Bernhard Leeb. Dynamics on flag manifolds: domains of proper discontinuity and cocompactness , Geometry and Topology 22:1 (2018) 157--234 DOI:10.2140/gt.2018.22.157 Arxiv version: 1306.3837
with Michael Kapovich and Bernhard Leeb. Anosov subgroups: Dynamical and geometric characterizations. European Journal of Mathematics 3:4 (2017) 808--898 DOI: 10.1007/s40879-017-0192-y, Arxiv version: 1703.01647
Hyperbolic polygons of minimal perimeter in punctured discs, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) (5) 18 (2018), no. 3, 831–844. DOI: 10.2422/2036-2145.201609_017, Arxiv version: arXiv:1609.08460.
with L. Paoluzzi. Invariant character varieties of hyperbolic knots with symmetries , Math. Proc. Cambridge Philos. Soc. 165 (2018), no. 2, 193–208. DOI: 10.1017/S0305004117000391 arXiv:1505.0105
with M. Heusener and Vicente Muñoz The SL(3,C)-character variety of the figure eight knot , arXiv:1505.04451 Illinois Journal of Mathematics 60 (2016), no. 1, 55-98.
with Michael Kapovich and Bernhard Leeb. Some recent results on Anosov representations. Transform. Groups 21 (2016), no. 4, 1105–1121. DOI:10.1007/s00031-016-9393-6
with Vicente Muñoz Geometry of the SL(3,C)-character variety of torus knots , Algebraic and Geometric Topology 16 (2016) 397-426. DOI:10.2140/agt.2016.16.397 (arXiv version)
with M. Heusener Representations of knot groups into SL(n,C) and twisted Alexander polynomials , Pacific J of Math Vol. 277 (2015), No. 2, 313–354 DOI:10.2140/pjm.2015.277.313
Local and infinitesimal rigidity of representations of hyperbolic three manifolds. RIMS Kôkyûroku, Kyoto University Vol 1836 (2013), 154-177
Actions of hyperbolic three-manifold groups on complex projective space. RIMS Kôkyûroku, Kyoto University Vol 1836 (2013), 138-153
with Pere Menal-Ferrer. . Higher dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds , J. of Topology (2014) 7 (1): 69-119. DOI:10.1112/jtopol/jtt024
with L. Paoluzzi. Non-standard components of the character variety for a family of Montesinos knots , Proc. London Math. Soc., (2013) 107 (3): 655-679 DOI:10.1112/plms/pds094,
Regenerating hyperbolic cone 3-manifolds from dimension 2 , Annales de l'Institut Fourier 63 no. 5 (2013), p. 1971-2015. DOI:10.5802/aif.2820
with Pere Menal-Ferrer. . Local coordinates for SL(n,C) character varieties of finite volume hyperbolic 3-manifolds , Ann. Blaise Pascal 19 no. 1 (2012), p. 107-122
with Pere Menal-Ferrer. . Mutation and SL(2,C)-Reidemeister torsion for hyperbolic knots , Algebr. Geom. Topol. 12 (2012) 2049–2067. DOI: 10.2140/agt.2012.12.2049
with Pere Menal-Ferrer. . Twisted cohomology for hyperbolic three manifolds , Osaka J. of Math. 49, n. 3 (2012), 741-769
with M. Heusener. Infinitesimal projective rigidity under Dehn filling , Geometry and Topology 15 (2011) 2017–2071. DOI: 10.2140/gt.2011.15.2017
Hyperbolic polygons of minimal perimeter with given angles , Geom. Dedicata Vol 156 (2012), No. 1, 165-170. DOI: 10.1007/s10711-011-9597-9
with L. Paoluzzi. Conway spheres as ideal points of the character variety, Math. Annalen, Vol. 354 (2012), No.2, 707-726 DOI: 10.1007/s00208-011-0748-y
with Laurent Bessières, Gérard Besson, Michel Boileau, Sylvain Maillot. Geometrisation of 3-Manifolds , EMS Tracts in Mathematics Vol. 13, September 2010.
with Laurent Bessières, Gérard Besson, Michel Boileau, Sylvain Maillot. Collapsing irreducible 3-manifolds with nontrivial fundamental group , Invent. Math. . Vol 179 (2010), No. 2, 435-460.
with L. Paoluzzi. Hyperbolic isometries versus symmetries of links, Topology Appl. 156 (2009), 1140-1147
Geometrization of three manifolds and Perelman’s proof. Rev. R. Acad. Cien. Serie A. Mat. Vol. 101 (2008), No. 1, 101-125
with Stefano Francaviglia. Rigidity of representations in SO(4,1) for Dehn fillings on 2-bridge knots. Pacific J. of Math. Vol. 238 (2008), No. 2, 249-274
with D. Cooper. Non compact Euclidan cone 3-manifolds with cone angles less than 2 pi. Geometry and Topology Monographs , 14 (2008) 173–192
with H. Weiss. Deforming Euclidean cone 3-manifolds . Geometry and Topology, Vol. 11 (2007), 1507-1538.
with M. Boileau, B. Leeb.Geometrization of 3-dimensional orbifolds Annals of Math. 162 (2005), no. 1, 195--250
with M. Heusener. Deformations of reducible representations of 3-manifold groups into PSL(2,C). Algebraic and Geometric Topology 5 (2005), 965--997.
Spherical cone structures on 2-bridge knots and links. Kobe J. Math. 21 (2004), no. 1-2, 61—70.
with M. Heusener. The variety of characters in PSL(2,C). Bol. Soc Mat. Mex. 10 (2004) no. 3.
Mayberry-Murasugi's formula for links in homology 3-spheres. Proc. Amer. Math. Soc. 132 (2004), no. 11, 3423--3431
with M. Boileau, and S. Maillot, Three-Dimensional Orbifolds and their Geometric Structures Panoramas et Synthèses, 15. Société Mathématique de France, Paris, 2003. viii+167 pp.
Regenerating hyperbolic cone structures from Nil. Geometry and Topology, Vol. 6 (2002), 815-852.
with Warren Dicks. On the Hausdorff dimension of the Gieseking fractal. Topology and its Applications) 126 (2002), 169--186
with M. Heusener and E. Suárez. Regenerating singular hyperbolic structures from Sol. J. Differential Geom. 59 (2001), 439-478
with M. Boileau, B. Leeb. Unifomization of small 3-orbifolds C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 57--62.
with M. Boileau. Geometrization of 3-orbifolds of cyclic type Astérisque 272, (2001) Free link in Nundam (the French digital mathematics library)
with M. Heusener and E. Suárez. Deformations of reducible representations of 3-manifold groups into SL(2,C) J. Reine Angew. Math. 530 (2001), 191--227.
with C. Petronio. Negatively oriented ideal triangulations and a proof of Thurston's hyperbolic Dehn filling theorem. J. Porti, Expo. Math. 18 (2000), no. 1, 1--35.
with R. C. Alperin and Warren Dicks. The boundary of the Gieseking tree in hyperbolic three-space. Topology Appl. 93 (1999), no. 3, 219--259.
with Warren Dicks. Expressing a number as the sum of two coprime squares. Dedicated to the memory of Fernando Serrano. Collect. Math. 49 (1998), no. 2-3, 283--291.
Regenerating hyperbolic and spherical cone structures from Euclidean ones. Topology 37 (1998), no. 2, 365--392.
Torsion de Reidemeister pour les variétés hyperboliques. Mem. Amer. Math. Soc. 128 (1997), no. 612, x+139 pp.
Torsion de Reidemeister pour les variétés hyperboliques. C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 1, 59--64.