Algebraic & Geometric Topology Volume 21, issue 6 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

Augmentations and link group representations

Honghao Gao

Algebraic & Geometric Topology 21 (2021) 2857–2898

DOI: 10.2140/agt.2021.21.2857

Bibliography

1	M Aganagic, T Ekholm, L Ng, C Vafa, Topological strings, D–model, and knot contact homology, Adv. Theor. Math. Phys. 18 (2014) 827 MR3277674
2	J W Alexander, A lemma on systems of knotted curves, Proc. Natl. Acad. Sci. USA 9 (1923) 93
3	L Ben Abdelghani, M Heusener, Irreducible representations of knot groups into SL(n, ℂ), Publ. Mat. 61 (2017) 363 MR3677866
4	S Boyer, X Zhang, Every nontrivial knot in S³ has nontrivial A–polynomial, Proc. Amer. Math. Soc. 133 (2005) 2813 MR2146231
5	K Cieliebak, T Ekholm, J Latschev, L Ng, Knot contact homology, string topology, and the cord algebra, J. Éc. Polytech. Math. 4 (2017) 661 MR3665612
6	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
7	C R Cornwell, KCH representations, augmentations, and A–polynomials, J. Symplectic Geom. 15 (2017) 983 MR3734607
8	M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. 117 (1983) 109 MR683804
9	N M Dunfield, S Garoufalidis, Non-triviality of the A–polynomial for knots in S³, Algebr. Geom. Topol. 4 (2004) 1145 MR2113900
10	T Ekholm, J B Etnyre, L Ng, M G Sullivan, Knot contact homology, Geom. Topol. 17 (2013) 975 MR3070519
11	T Ekholm, L Ng, V Shende, A complete knot invariant from contact homology, Invent. Math. 211 (2018) 1149 MR3763406
12	Y Eliashberg, Invariants in contact topology, from: "Proceedings of the International Congress of Mathematicians, II" (editors G Fischer, U Rehmann), Deutsche Mathematiker Vereinigung (1998) 327 MR1648083
13	Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, from: "Visions in mathematics" (editors N Alon, J Bourgain, A Connes, M Gromov, V Milman), Birkhäuser (= GAFA special volume) (2000) 560 MR1826267
14	H Gao, Radon transform for sheaves, preprint (2017) arXiv:1712.06453
15	H Gao, Simple sheaves for knot conormals, J. Symplectic Geom. 18 (2020) 1027 MR4174293
16	S Garoufalidis, D P Thurston, C K Zickert, The complex volume of SL(n, ℂ)–representations of 3–manifolds, Duke Math. J. 164 (2015) 2099 MR3385130
17	S Guillermou, M Kashiwara, P Schapira, Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems, Duke Math. J. 161 (2012) 201 MR2876930
18	A Guilloux, P Will, On SL(3, ℂ)–representations of the Whitehead link group, Geom. Dedicata 202 (2019) 81 MR4001809
19	M Heusener, V Muñoz, J Porti, The SL(3, ℂ)–character variety of the figure eight knot, Illinois J. Math. 60 (2016) 55 MR3665172
20	M Kashiwara, P Schapira, Sheaves on manifolds, 292, Springer (1990) MR1074006
21	P B Kronheimer, T S Mrowka, Dehn surgery, the fundamental group and SU(2), Math. Res. Lett. 11 (2004) 741 MR2106239
22	K Mishachev, The N–copy of a topologically trivial Legendrian knot, J. Symplectic Geom. 1 (2003) 659 MR2039159
23	V Muñoz, J Porti, Geometry of the SL(3, ℂ)–character variety of torus knots, Algebr. Geom. Topol. 16 (2016) 397 MR3470704
24	D Nadler, Microlocal branes are constructible sheaves, Selecta Math. 15 (2009) 563 MR2565051
25	D Nadler, E Zaslow, Constructible sheaves and the Fukaya category, J. Amer. Math. Soc. 22 (2009) 233 MR2449059
26	L Ng, Knot and braid invariants from contact homology, I, Geom. Topol. 9 (2005) 247 MR2116316
27	L Ng, Knot and braid invariants from contact homology, II, Geom. Topol. 9 (2005) 1603 MR2175153
28	L Ng, Framed knot contact homology, Duke Math. J. 141 (2008) 365 MR2376818
29	L Ng, A topological introduction to knot contact homology, from: "Contact and symplectic topology" (editors F Bourgeois, V Colin, A Stipsicz), Bolyai Soc. Math. Stud. 26, János Bolyai Math. Soc. (2014) 485 MR3220948
30	L Ng, D Rutherford, V Shende, S Sivek, E Zaslow, Augmentations are sheaves, Geom. Topol. 24 (2020) 2149 MR4194293
31	Y Ni, X Zhang, Detection of knots and a cabling formula for A–polynomials, Algebr. Geom. Topol. 17 (2017) 65 MR3604373
32	D Rolfsen, Knots and links, 7, Publish or Perish (1976) MR0515288
33	K Sackel, Augmentations are colorings, MR3861709
34	V Shende, D Treumann, E Zaslow, Legendrian knots and constructible sheaves, Invent. Math. 207 (2017) 1031 MR3608288
35	P Vogel, Representation of links by braids: a new algorithm, Comment. Math. Helv. 65 (1990) 104 MR1036132
36	F Waldhausen, On irreducible 3–manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR224099
37	S Yamada, The minimal number of Seifert circles equals the braid index of a link, Invent. Math. 89 (1987) 347 MR894383