Volume 15, issue 4 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
Braids, complex volume and cluster algebras

Kazuhiro Hikami and Rei Inoue

Algebraic & Geometric Topology 15 (2015) 2175–2194
Bibliography
1 J Cho, H Kim, S Kim, Optimistic limits of Kashaev invariants and complex volumes of hyperbolic links, J. Knot Theory Ramifications 23 (2014) 1450049 MR3268985
2 J Cho, J Murakami, The complex volumes of twist knots via colored Jones polynomials, J. Knot Theory Ramifications 19 (2010) 1401 MR2746194
3 J Cho, J Murakami, Y Yokota, The complex volumes of twist knots, Proc. Amer. Math. Soc. 137 (2009) 3533 MR2515423
4 P Dehornoy, I Dynnikov, D Rolfsen, B Wiest, Ordering braids, Math. Surveys and Monographs 148, Amer. Math. Soc. (2008) MR2463428
5 I A Dynnikov, On a Yang–Baxter mapping and the Dehornoy ordering, Uspekhi Mat. Nauk 57 (2002) 151 MR1918864
6 V V Fock, A B Goncharov, Dual Teichmüller and lamination spaces, from: "Handbook of Teichmüller theory, Volume I" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys., Eur. Math. Soc. (2007) 647 MR2349682
7 V V Fock, A B Goncharov, Cluster ensembles, quantization and the dilogarithm, Ann. Sci. Éc. Norm. Supér. 42 (2009) 865 MR2567745
8 S Fomin, M Shapiro, D Thurston, Cluster algebras and triangulated surfaces, I: Cluster complexes, Acta Math. 201 (2008) 83 MR2448067
9 S Fomin, A Zelevinsky, Cluster algebras, I: Foundations, J. Amer. Math. Soc. 15 (2002) 497 MR1887642
10 S Fomin, A Zelevinsky, Cluster algebras, IV: Coefficients, Compos. Math. 143 (2007) 112 MR2295199
11 K Hikami, Hyperbolic structure arising from a knot invariant, Internat. J. Modern Phys. A 16 (2001) 3309 MR1848458
12 K Hikami, R Inoue, Braiding operator via quantum cluster algebra, J. Phys. A 47 (2014) 474006, 21 MR3279997
13 K Hikami, R Inoue, Cluster algebra and complex volume of once-punctured torus bundles and $2$–bridge links, J. Knot Theory Ramifications 23 (2014) 1450006, 33 MR3190130
14 K Hikami, A N Kirillov, Torus knot and minimal model, Phys. Lett. B 575 (2003) 343 MR2044711
15 A Inoue, Y Kabaya, Quandle homology and complex volume, Geom. Dedicata 171 (2014) 265 MR3226796
16 R M Kashaev, A link invariant from quantum dilogarithm, Modern Phys. Lett. A 10 (1995) 1409 MR1341338
17 R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269 MR1434238
18 R M Kashaev, On the spectrum of Dehn twists in quantum Teichmüller theory, from: "Physics and combinatorics" (editors A N Kirillov, N Liskova), World Sci. Publ. (2001) 63 MR1872252
19 R M Kashaev, O Tirkkonen, A proof of the volume conjecture on torus knots, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 269 (2000) 262, 370 MR1805865
20 H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
21 K Nagao, Y Terashima, M Yamazaki, Hyperbolic $3$–manifolds and cluster algebras, arXiv:1112.3106
22 T Nakanishi, Periodicities in cluster algebras and dilogarithm identities, from: "Representations of algebras and related topics" (editors A Skowroński, K Yamagata), Eur. Math. Soc. (2011) 407 MR2931902
23 W D Neumann, Extended Bloch group and the Cheeger–Chern–Simons class, Geom. Topol. 8 (2004) 413 MR2033484
24 D Thurston, Hyperbolic volume and the Jones polynomial (1999)
25 W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
26 J Weeks, Computation of hyperbolic structures in knot theory, from: "Handbook of knot theory" (editors W Menasco, M Thistlethwaite), Elsevier (2005) 461 MR2179268
27 Y Yokota, On the complex volume of hyperbolic knots, J. Knot Theory Ramifications 20 (2011) 955 MR2819177
28 D Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function, Topology 40 (2001) 945 MR1860536
29 C K Zickert, The volume and Chern–Simons invariant of a representation, Duke Math. J. 150 (2009) 489 MR2582103