Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Dimension of representation and character varieties for two- and three-orbifolds

Joan Porti

Algebraic & Geometric Topology 22 (2022) 1905–1967
Bibliography
1 M Acosta, Character varieties for real forms of classical complex groups, preprint (2019) arXiv:1908.10704
2 D Alessandrini, G S Lee, F Schaffhauser, Hitchin components for orbifolds, J. Eur. Math. Soc. (2022)
3 M Boileau, S Maillot, J Porti, Three-dimensional orbifolds and their geometric structures, 15, Soc. Math. France (2003) MR2060653
4 M Brittenham, Y Q Wu, The classification of exceptional Dehn surgeries on 2–bridge knots, Comm. Anal. Geom. 9 (2001) 97 MR1807953
5 K Bromberg, Rigidity of geometrically finite hyperbolic cone-manifolds, Geom. Dedicata 105 (2004) 143 MR2057249
6 H Cartan, Quotient d’une variété analytique par un groupe discret d’automorphismes, Séminaire Henri Cartan 6 (1953–1954)
7 A Casimiro, C Florentino, S Lawton, A Oliveira, Topology of moduli spaces of free group representations in real reductive groups, Forum Math. 28 (2016) 275 MR3466569
8 S Choi, H Jung, Symplectic coordinates on the deformation spaces of convex projective structures on 2–orbifolds, preprint (2020) arXiv:2007.13285
9 S Choi, G S Lee, L Marquis, Deformations of convex real projective manifolds and orbifolds, from: "Handbook of group actions, III" (editors L Ji, A Papadopoulos, S T Yau), Adv. Lect. Math. 40, International (2018) 263 MR3888622
10 I Dolgachev, Lectures on invariant theory, 296, Cambridge Univ. Press (2003) MR2004511
11 W D Dunbar, Nonfibering spherical 3–orbifolds, Trans. Amer. Math. Soc. 341 (1994) 121 MR1118824
12 E Falbel, A Guilloux, Dimension of character varieties for 3–manifolds, Proc. Amer. Math. Soc. 145 (2017) 2727 MR3626524
13 E Falbel, A Guilloux, P V Koseleff, F Rouillier, M Thistlethwaite, Character varieties for SL(, ) : the figure eight knot, Exp. Math. 25 (2016) 219 MR3463570
14 W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math. 54 (1984) 200 MR762512
15 C Gordon, Dehn surgery and 3–manifolds, from: "Low dimensional topology" (editors T S Mrowka, P S Ozsváth), IAS/Park City Math. Ser. 15, Amer. Math. Soc. (2009) 21 MR2503492
16 A Guilloux, P Will, On SL(3, )–representations of the Whitehead link group, Geom. Dedicata 202 (2019) 81 MR4001809
17 K Guruprasad, J Huebschmann, L Jeffrey, A Weinstein, Group systems, groupoids, and moduli spaces of parabolic bundles, Duke Math. J. 89 (1997) 377 MR1460627
18 R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
19 M Heusener, V Muñoz, J Porti, The SL(3, )–character variety of the figure eight knot, Illinois J. Math. 60 (2016) 55 MR3665172
20 M Heusener, J Porti, Representations of knot groups into SLn() and twisted Alexander polynomials, Pacific J. Math. 277 (2015) 313 MR3402353
21 M Heusener, J Porti, Holomorphic volume forms on representation varieties of surfaces with boundary, Ann. H. Lebesgue 3 (2020) 341 MR4113650
22 M Heusener, J Porti, E Suárez Peiró, Deformations of reducible representations of 3–manifold groups into SL2(), J. Reine Angew. Math. 530 (2001) 191 MR1807271
23 D Johnson, J J Millson, Deformation spaces associated to compact hyperbolic manifolds, from: "Discrete groups in geometry and analysis" (editor R Howe), Progr. Math. 67, Birkhäuser (1987) 48 MR900823
24 M Kapovich, Hyperbolic manifolds and discrete groups, 183, Birkhäuser (2001) MR1792613
25 S Lawton, Generators, relations and symmetries in pairs of 3 × 3 unimodular matrices, J. Algebra 313 (2007) 782 MR2329569
26 S Lawton, Poisson geometry of SL(3, )–character varieties relative to a surface with boundary, Trans. Amer. Math. Soc. 361 (2009) 2397 MR2471924
27 D D Long, M B Thistlethwaite, The dimension of the Hitchin component for triangle groups, Geom. Dedicata 200 (2019) 363 MR3956201
28 B Martelli, C Petronio, Dehn filling of the “magic” 3–manifold, Comm. Anal. Geom. 14 (2006) 969 MR2287152
29 P Menal-Ferrer, J Porti, Local coordinates for SL(n, )–character varieties of finite-volume hyperbolic 3–manifolds, Ann. Math. Blaise Pascal 19 (2012) 107 MR2978315
30 P Menal-Ferrer, J Porti, Twisted cohomology for hyperbolic three manifolds, Osaka J. Math. 49 (2012) 741 MR2993065
31 J Porti, Torsion de Reidemeister pour les variétés hyperboliques, 612, Amer. Math. Soc. (1997) MR1396960
32 J Porti, S Tillmann, Projective structures on a hyperbolic 3–orbifold, Acta Math. Vietnam. 46 (2021) 347 MR4264240
33 J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (1994) MR1299730
34 R W Richardson, Commuting varieties of semisimple Lie algebras and algebraic groups, Compos. Math. 38 (1979) 311 MR535074
35 A S Sikora, Generating sets for coordinate rings of character varieties, J. Pure Appl. Algebra 217 (2013) 2076 MR3057078
36 R Steinberg, Regular elements of semisimple algebraic groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965) 49 MR180554
37 P Tauvel, R W T Yu, Lie algebras and algebraic groups, Springer (2005) MR2146652
38 W Thurston, Geometry and topology of three-manifolds, lecture notes (1980)
39 A Weil, Remarks on the cohomology of groups, Ann. of Math. 80 (1964) 149 MR169956