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Reidemeister torsion form on character varieties

Léo Bénard

Algebraic & Geometric Topology 20 (2020) 2821–2884
DOI: 10.2140/agt.2020.20.2821
Bibliography
1 L Bénard, Torsion function on character varieties, preprint (2017) arXiv:1711.08781
2 L Bénard, Reidemeister torsion on character varieties, PhD thesis, Sorbonne Université (2018)
3 L Bénard, A Conway, A multivariable Casson–Lin type invariant, Ann. Inst. Fourier (Grenoble) 70 (2020) 1029
4 R W Berger, Report on the torsion of the differential module of an algebraic curve, from: "Algebraic geometry and its applications" (editor C L Bajaj), Springer (1994) 285 MR1272036
5 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
6 G Burde, Darstellungen von Knotengruppen, Math. Ann. 173 (1967) 24 MR212787
7 T A Chapman, Topological invariance of Whitehead torsion, Amer. J. Math. 96 (1974) 488 MR391109
8 M Chu, Detecting essential surfaces as intersections in the character variety, Algebr. Geom. Topol. 17 (2017) 2893 MR3704247
9 M M Cohen, A course in simple-homotopy theory, 10, Springer (1973) MR0362320
10 D Cooper, M Culler, H Gillet, D D Long, P B Shalen, Plane curves associated to character varieties of 3–manifolds, Invent. Math. 118 (1994) 47 MR1288467
11 M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. 125 (1987) 237 MR881270
12 M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. 117 (1983) 109 MR683804
13 M Culler, P B Shalen, Bounded, separating, incompressible surfaces in knot manifolds, Invent. Math. 75 (1984) 537 MR735339
14 J F Davis, P Kirk, Lecture notes in algebraic topology, 35, Amer. Math. Soc. (2001) MR1841974
15 J Dubois, Torsion de Reidemeister non abélienne et forme volume sur l’espace des représentations du groupe d’un nœud, PhD thesis, Université Blaise Pascal, Clermont-Ferrand II (2003)
16 J Dubois, Non abelian twisted Reidemeister torsion for fibered knots, Canad. Math. Bull. 49 (2006) 55 MR2198719
17 J Dubois, S Garoufalidis, Rationality of the SL(2, )–Reidemeister torsion in dimension 3, Topology Proc. 47 (2016) 115 MR3355211
18 J Dubois, V Huynh, Y Yamaguchi, Non-abelian Reidemeister torsion for twist knots, J. Knot Theory Ramifications 18 (2009) 303 MR2514847
19 N M Dunfield, S Friedl, N Jackson, Twisted Alexander polynomials of hyperbolic knots, Exp. Math. 21 (2012) 329 MR3004250
20 S Friedl, T Kitayama, M Nagel, Representation varieties detect essential surfaces, Math. Res. Lett. 25 (2018) 803 MR3847335
21 C D Frohman, J Kania-Bartoszynska, Dubois torsion, A–polynomial and quantum invariants, Quantum Topol. 4 (2013) 187 MR3032821
22 W Fulton, Algebraic curves: an introduction to algebraic geometry, Benjamin (1969) MR0313252
23 I M Gelfand, M M Kapranov, A V Zelevinsky, Discriminants, resultants, and multidimensional determinants, Birkhäuser (1994) MR1264417
24 A Hatcher, W Thurston, Incompressible surfaces in 2–bridge knot complements, Invent. Math. 79 (1985) 225 MR778125
25 M Heusener, J Porti, Representations of knot groups into SLn() and twisted Alexander polynomials, Pacific J. Math. 277 (2015) 313 MR3402353
26 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
27 D Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann. 36 (1890) 473 MR1510634
28 T Kitano, Reidemeister torsion of Seifert fibered spaces for SL(2; )–representations, Tokyo J. Math. 17 (1994) 59 MR1279569
29 T Kitano, Reidemeister torsion of the figure-eight knot exterior for SL(2; )–representations, Osaka J. Math. 31 (1994) 523 MR1309401
30 H Kraft, C Procesi, Classical invariant theory: a primer, preprint (1996)
31 Q Liu, Algebraic geometry and arithmetic curves, 6, Oxford Univ. Press (2002) MR1917232
32 A Lubotzky, A R Magid, Varieties of representations of finitely generated groups, 336, Amer. Math. Soc. (1985) MR818915
33 J Marché, Character varieties in SL2 and Kauffman skein algebras, preprint (2015) arXiv:1510.09107
34 J Marché, M Wolff, The parallelogram identity on groups and deformations of the trivial character in SL2(), J. Éc. Polytech. Math. 7 (2020) 263
35 J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358 MR196736
36 D Mumford, J Fogarty, F Kirwan, Geometric invariant theory, 34, Springer (1994) MR1304906
37 W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
38 J Park, Half-density volumes of representation spaces of some 3–manifolds and their application, Duke Math. J. 86 (1997) 493 MR1432306
39 J Porti, Torsion de Reidemeister pour les variétés hyperboliques, 612, Amer. Math. Soc. (1997) MR1396960
40 C Procesi, A formal inverse to the Cayley–Hamilton theorem, J. Algebra 107 (1987) 63 MR883869
41 J H Przytycki, Incompressibility of surfaces after Dehn surgery, Michigan Math. J. 30 (1983) 289 MR725782
42 J H Przytycki, A S Sikora, On skein algebras and Sl2()–character varieties, Topology 39 (2000) 115 MR1710996
43 G de Rham, Introduction aux polynômes d’un nœud, Enseign. Math. 13 (1967) 187 MR240804
44 K Saito, Character variety of representations of a finitely generated group in SL2, from: "Topology and Teichmüller spaces" (editors S Kojima, Y Matsumoto, K Saito, M Seppälä), World Sci. (1996) 253 MR1659663
45 J P Serre, Arbres, amalgames, SL2, 46, Soc. Math. France (1977) MR0476875
46 P B Shalen, Representations of 3–manifold groups, from: "Handbook of geometric topology" (editors R J Daverman, R B Sher), North-Holland (2002) 955 MR1886685
47 W P Thurston, Three-dimensional geometry and topology, I, 35, Princeton Univ. Press (1997) MR1435975
48 S Tillmann, Finding hyperbolic structures of and surfaces in 3–manifolds, course notes (2003)
49 A T Tran, Twisted Alexander polynomials of genus one two-bridge knots, Kodai Math. J. 41 (2018) 86 MR3777388
50 V Turaev, Introduction to combinatorial torsions, Birkhäuser (2001) MR1809561
51 A Weil, Remarks on the cohomology of groups, Ann. of Math. 80 (1964) 149 MR169956
52 E Witten, On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991) 153 MR1133264
53 S Yoon, A vanishing identity on adjoint Reidemeister torsions, preprint (2020) arXiv:2002.12576