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Tangent cones and local geometry of the representation and character varieties of knot groups

Leila Ben Abdelghani

Algebraic & Geometric Topology 10 (2010) 433–463

DOI: 10.2140/agt.2010.10.433

Bibliography
1 M Artin, On the solutions of analytic equations, Invent. Math. 5 (1968) 277–291 MR0232018
2 L Ben Abdelghani, Arcs de représentations du groupe d'un noeud dans un groupe de Lie, PhD thesis, Université de Bourgogne (1998)
3 L Ben Abdelghani, Espace des représentations du groupe d'un nœ ud classique dans un groupe de Lie, Ann. Inst. Fourier (Grenoble) 50 (2000) 1297–1321 MR1799747
4 L Ben Abdelghani, D Lines, Involutions on knot groups and varieties of representations in a Lie group, J. Knot Theory Ramifications 11 (2002) 81–104 MR1885749
5 R C Blanchfield, Intersection theory of manifolds with operators with applications to knot theory, Ann. of Math. (2) 65 (1957) 340–356 MR0085512
6 N Bourbaki, Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie, Actualités Scientifiques et Industrielles 1349, Hermann (1972) 320 MR0573068
7 S Boyer, On the local structure of SL(2,C)–character varieties at reducible characters, Topology Appl. 121 (2002) 383–413 MR1909000
8 K S Brown, Cohomology of groups, Graduate Texts in Math. 87, Springer (1982) MR672956
9 G Burde, Darstellungen von Knotengruppen, Math. Ann. 173 (1967) 24–33 MR0212787
10 G Burde, H Zieschang, Knots, de Gruyter Studies in Math. 5, de Gruyter (2003) MR1959408
11 M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. (2) 117 (1983) 109–146 MR683804
12 C D Frohman, E P Klassen, Deforming representations of knot groups in SU(2), Comment. Math. Helv. 66 (1991) 340–361 MR1120651
13 C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371–415 MR965210
14 C M Herald, Existence of irreducible representations for knot complements with nonconstant equivariant signature, Math. Ann. 309 (1997) 21–35 MR1467643
15 M Heusener, J Kroll, Deforming abelian SU(2)–representations of knot groups, Comment. Math. Helv. 73 (1998) 480–498 MR1633375
16 M Heusener, J Porti, Deformations of reducible representations of 3–manifold groups into PSL2(C), Algebr. Geom. Topol. 5 (2005) 965–997 MR2171800
17 M Heusener, J Porti, E Suárez Peiró, Deformations of reducible representations of 3–manifold groups into SL2(C), J. Reine Angew. Math. 530 (2001) 191–227 MR1807271
18 E P Klassen, Representations of knot groups in SU(2), Trans. Amer. Math. Soc. 326 (1991) 795–828 MR1008696
19 A Lubotzky, A R Magid, Varieties of representations of finitely generated groups, Mem. Amer. Math. Soc. 58 (1985) MR818915
20 A Nijenhuis, R W Richardson Jr., Deformations of homomorphisms of Lie groups and Lie algebras, Bull. Amer. Math. Soc. 73 (1967) 175–179 MR0204575
21 G de Rham, Introduction aux polynômes d'un nœ ud, Enseignement Math. (2) 13 (1967) MR0240804
22 D J Shors, Deforming reducible representations of knot groups in SL2(\C), PhD thesis, University of California Los Angeles (1991)
23 A Weil, Remarks on the cohomology of groups, Ann. of Math. (2) 80 (1964) 149–157 MR0169956
24 W Whitten, Knot complements and groups, Topology 26 (1987) 41–44 MR880506