Algebraic & Geometric Topology Volume 10, issue 1 (2010)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

To Appear

Other MSP Journals

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 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 n\oe ud classique dans un groupe de Lie, Ann. Inst. Fourier (Grenoble) 50 (2000) 1297 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 MR1885749
5	R C Blanchfield, Intersection theory of manifolds with operators with applications to knot theory, Ann. of Math. $(2)$ 65 (1957) 340 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 $\mathrm{SL}(2,\mathbb{C})$–character varieties at reducible characters, Topology Appl. 121 (2002) 383 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 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 MR683804
12	C D Frohman, E P Klassen, Deforming representations of knot groups in $\mathrm{SU}(2)$, Comment. Math. Helv. 66 (1991) 340 MR1120651
13	C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
14	C M Herald, Existence of irreducible representations for knot complements with nonconstant equivariant signature, Math. Ann. 309 (1997) 21 MR1467643
15	M Heusener, J Kroll, Deforming abelian $\mathrm{SU}(2)$–representations of knot groups, Comment. Math. Helv. 73 (1998) 480 MR1633375
16	M Heusener, J Porti, Deformations of reducible representations of $3$–manifold groups into $\mathrm{PSL}_2(\mathbb C)$, Algebr. Geom. Topol. 5 (2005) 965 MR2171800
17	M Heusener, J Porti, E Suárez Peiró, Deformations of reducible representations of $3$–manifold groups into $\mathrm{SL}_2(\mathbf{C})$, J. Reine Angew. Math. 530 (2001) 191 MR1807271
18	E P Klassen, Representations of knot groups in $\mathrm{SU}(2)$, Trans. Amer. Math. Soc. 326 (1991) 795 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 MR0204575
21	G de Rham, Introduction aux polynômes d'un n\oe ud, Enseignement Math. $(2)$ 13 (1967) MR0240804
22	D J Shors, Deforming reducible representations of knot groups in $\mathrm{SL}_2({\C})$, PhD thesis, University of California Los Angeles (1991)
23	A Weil, Remarks on the cohomology of groups, Ann. of Math. $(2)$ 80 (1964) 149 MR0169956
24	W Whitten, Knot complements and groups, Topology 26 (1987) 41 MR880506