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[BL99] Bismut, Jean-Michel; Labourie, François Symplectic geometry and the Verlinde formulas, Surveys in differential geometry. Differential geometry inspired by string theory (Yau, Shing-Tung, ed.) (Surveys in Differential Geometry) Volume 5, International Press, 1999, pp. 97-311 | DOI | MR | Zbl

[Bén16] Bénard, Léo Torsion function on character varieties (2016) (https://arxiv.org/abs/1612.06237, to appear in Algebraic & Geometric Topology)

[Bén17] Bénard, Léo Singularities of the Reidemeister torsion form on the character variety (2017) (https://arxiv.org/abs/1711.08781, to appear in Osaka Journal of Mathematics)

[DG16] Dubois, Jerôme; Garoufalidis, Stavros Rationality of the $\text{SL}(2,ℂ)$-Reidemeister torsion in dimension 3, Topol. Proc., Volume 47 (2016), pp. 115-134 | MR | Zbl

[FH91] Fulton, William; Harris, Joe Representation theory. A first course, Graduate Texts in Mathematics, Volume 129, Springer, 1991, xvi+551 pages | DOI | Zbl

[FK97] Fricke, Robert; Klein, Felix Vorlesungen über die Theorie der automorphen Functionen. Erster Band; Die gruppentheoretischen Grundlagen, Leipzig: B. G. Teubner. XIV+634 pages, 1897 | Zbl

[Fra36] Franz, Wolfgang Torsionsideale, Torsionsklassen und Torsion, J. Reine Angew. Math., Volume 176 (1936), pp. 113-124 | MR | Zbl

[Fri96] Fricke, Robert Ueber die Theorie der automorphen Modulgruppen, Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl., Volume 1896 (1896), pp. 91-101 | Zbl

[GAMA93] González-Acuña, Francisco Javier; Montesinos-Amilibia, José María On the character variety of group representations in $\text{SL}(2,ℂ)$ and $\text{PSL}(2,ℂ)$, Math. Z., Volume 214 (1993) no. 4, pp. 627-652 | DOI | MR | Zbl

[GHJW97] Guruprasad, Krishnamurthi; Huebschmann, Johannes; Jeffrey, Lisa C.; Weinstein, Alan David Group systems, groupoids, and moduli spaces of parabolic bundles, Duke Math. J., Volume 89 (1997) no. 2, pp. 377-412 | DOI | MR

[Gol84] Goldman, William M. The symplectic nature of fundamental groups of surfaces, Adv. Math., Volume 54 (1984) no. 2, pp. 200-225 | DOI | MR | Zbl

[Gol86] Goldman, William M. Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math., Volume 85 (1986) no. 2, pp. 263-302 | DOI | MR | Zbl

[Gol04] Goldman, William M. The complex-symplectic geometry of $\text{SL}(2,ℂ)$-characters over surfaces, Algebraic groups and arithmetic (Dani, Shrikrishna Gopalrao, ed.), Tata Institute of Fundamental Research, 2004, pp. 375-407

[Gol09] Goldman, William M. Trace coordinates on Fricke spaces of some simple hyperbolic surfaces, Handbook of Teichmüller theory. Vol. II (Papadopoulos, Athanase, ed.) (IRMA Lectures in Mathematics and Theoretical Physics) Volume 13, European Mathematical Society, 2009, pp. 611-684 | DOI | MR | Zbl

[GW09] Goodman, Roe; Wallach, Nolan R. Symmetry, representations, and invariants, Graduate Texts in Mathematics, Volume 255, Springer, 2009, xx+716 pages (Based on the book “Representations and invariants of the classical groups” originally published by Cambridge University Press, 1998) | DOI | MR | Zbl

[Hum95] Humphreys, James E. Conjugacy classes in semisimple algebraic groups, Mathematical Surveys and Monographs, Volume 43, American Mathematical Society, 1995, xviii+196 pages | MR | Zbl

[JM87] Johnson, Dennis; Millson, John J. Deformation spaces associated to compact hyperbolic manifolds, Discrete groups in geometry and analysis. Papers in Honor of G.D. Mostow on his sixtieth birthday (Howe, Roger, ed.) (Progress in Mathematics) Volume 67, Birkhäuser, 1987, pp. 48-106 | DOI | MR | Zbl

[Kap01] Kapovich, Michael Hyperbolic manifolds and discrete groups, Progress in Mathematics, Volume 183, Birkhäuser, 2001, xxvi+467 pages | MR | Zbl

[Lab13] Labourie, François Lectures on representations of surface groups, Zürich Lectures in Advanced Mathematics, European Mathematical Society, 2013, viii+138 pages | DOI | Zbl

[Law07] Lawton, Sean Generators, relations and symmetries in pairs of $3\times 3$ unimodular matrices, J. Algebra, Volume 313 (2007) no. 2, pp. 782-801 | DOI | MR | Zbl

[Law09] Lawton, Sean Poisson geometry of $\text{SL}(3,ℂ)$-character varieties relative to a surface with boundary, Trans. Am. Math. Soc., Volume 361 (2009) no. 5, pp. 2397-2429 | DOI | MR | Zbl

[Law10] Lawton, Sean Algebraic independence in $\text{SL}(3,ℂ)$ character varieties of free groups, J. Algebra, Volume 324 (2010) no. 6, pp. 1383-1391 | DOI | MR | Zbl

[Mag80] Magnus, Wilhelm Rings of Fricke characters and automorphism groups of free groups, Math. Z., Volume 170 (1980) no. 1, pp. 91-103 | DOI | MR | Zbl

[Mar16] Marché, Julien Character varieties in ${SL}_2$ and Kauffman skein algebras, Topology, Geometry and Algebra of low dimensional manifolds (RIMS Kôkyûroku) Volume 1991 (2016), pp. 27-42 (http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1991-02.pdf)

[Mil62] Milnor, John W. A duality theorem for Reidemeister torsion, Ann. Math., Volume 76 (1962), pp. 137-147 | DOI | MR | Zbl

[Mil66] Milnor, John W. Whitehead torsion, Bull. Am. Math. Soc., Volume 72 (1966), pp. 358-426 | DOI | MR | Zbl

[New78] Newstead, Peter E. Introduction to moduli problems and orbit spaces, Lectures on Mathematics and Physics, Volume 51, Tata Institute of Fundamental Research, 1978, vi+183 pages | MR | Zbl

[OV90] Onishchik, Arkady L.; Vinberg, Èrnest B. Lie groups and algebraic groups, Springer Series in Soviet Mathematics, Springer, 1990, xx+328 pages (Translated from the Russian and with a preface by D. A. Leites) | DOI | MR

[Pop11] Popov, Vladimir L. Cross-sections, quotients, and representation rings of semisimple algebraic groups, Transform. Groups, Volume 16 (2011) no. 3, pp. 827-856 | DOI | MR | Zbl

[Por97] Porti, Joan Torsion de Reidemeister pour les variétés hyperboliques, Mem. Am. Math. Soc., Volume 128 (1997) no. 612, p. x+139 | MR | Zbl

[PS94] Algebraic geometry IV. Linear algebraic groups, invariant theory (Parshin, Alexei N.; Shafarevich, Igor’ Rostislavovich, eds.), Encyclopaedia of Mathematical Sciences, Volume 55, Springer, 1994, vi+284 pages (Translation from the Russian by G.A. Kandall.)

[Qui76] Quillen, Daniel Projective modules over polynomial rings, Invent. Math., Volume 36 (1976), pp. 167-171 | DOI | MR | Zbl

[Sik12] Sikora, Adam S. Character varieties, Trans. Am. Math. Soc., Volume 364 (2012) no. 10, pp. 5173-5208 | DOI | MR | Zbl

[Ste65] Steinberg, Robert Regular elements of semisimple algebraic groups, Publ. Math., Inst. Hautes Étud. Sci. (1965) no. 25, pp. 49-80 | DOI | MR | Zbl

[Ste74] Steinberg, Robert Conjugacy classes in algebraic groups, Lecture Notes in Mathematics, Volume 366, Springer, 1974, vi+159 pages (Notes by Vinay V. Deodhar) | MR | Zbl

[Sus76] Suslin, Andrei A. Projective modules over polynomial rings are free, Dokl. Akad. Nauk SSSR, Volume 229 (1976) no. 5, pp. 1063-1066 | MR | Zbl

[Tur86] Turaev, Vladimir G. Reidemeister torsion in knot theory, Usp. Mat. Nauk, Volume 41 (1986) no. 1(247), pp. 97-147 | MR | Zbl

[Vog89] Vogt, Henri Gustave Sur les invariants fondamentaux des équations différentielles linéaires du second ordre, Ann. Sci. Éc. Norm. Supér., Volume 6 (1889), pp. 3-72 | DOI | Numdam | Zbl

[Wit91] Witten, Edward On quantum gauge theories in two dimensions, Commun. Math. Phys., Volume 141 (1991) no. 1, pp. 153-209 | DOI | MR | Zbl

[Łoj91] Łojasiewicz, Stanisław Introduction to complex analytic geometry, Birkhäuser, 1991, xiv+523 pages (Translated from the Polish by Maciej Klimek) | DOI | Zbl