Volume 13, issue 6 (2013)

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

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

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
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
Topological invariants from nonrestricted quantum groups

Nathan Geer and Bertrand Patureau-Mirand

Algebraic & Geometric Topology 13 (2013) 3305–3363
Bibliography
1 Y Akutsu, T Deguchi, T Ohtsuki, Invariants of colored links, J. Knot Theory Ramifications 1 (1992) 161 MR1164114
2 S Baseilhac, R Benedetti, Quantum hyperbolic invariants of $3$–manifolds with $\mathrm{PSL}(2,\mathbb C)$–characters, Topology 43 (2004) 1373 MR2081430
3 S Baseilhac, R Benedetti, Quantum hyperbolic geometry, Algebr. Geom. Topol. 7 (2007) 845 MR2336244
4 J Bichon, Cosovereign Hopf algebras, J. Pure Appl. Algebra 157 (2001) 121 MR1812048
5 R Brown, Groupoids and van Kampen's theorem, Proc. London Math. Soc. 17 (1967) 385 MR0220279
6 V Chari, A Pressley, A guide to quantum groups, Cambridge Univ. Press (1994) MR1300632
7 F Costantino, N Geer, B Patureau-Mirand, Quantum invariants of $3$–manifolds via link surgery presentations and non-semi-simple categories arXiv:1202.3553
8 C De Concini, V G Kac, Representations of quantum groups at roots of $1$, from: "Operator algebras, unitary representations, enveloping algebras, and invariant theory" (editors A Connes, M Duflo, A Joseph, R Rentschler), Progr. Math. 92, Birkhäuser (1990) 471 MR1103601
9 C De Concini, V G Kac, C Procesi, Quantum coadjoint action, J. Amer. Math. Soc. 5 (1992) 151 MR1124981
10 C De Concini, V G Kac, C Procesi, Some remarkable degenerations of quantum groups, Comm. Math. Phys. 157 (1993) 405 MR1244875
11 C De Concini, C Procesi, N Reshetikhin, M Rosso, Hopf algebras with trace and representations, Invent. Math. 161 (2005) 1 MR2178656
12 N Geer, R Kashaev, V Turaev, Tetrahedral forms in monoidal categories and $3$–manifold invariants, J. Reine Angew. Math. 673 (2012) 69 MR2999129
13 N Geer, J Kujawa, B Patureau-Mirand, Generalized trace and modified dimension functions on ribbon categories, Selecta Math. 17 (2011) 453 MR2803849
14 N Geer, B Patureau-Mirand, Multivariable link invariants arising from $\mathfrak{sl}(2 | 1)$ and the Alexander polynomial, J. Pure Appl. Algebra 210 (2007) 283 MR2311186
15 N Geer, B Patureau-Mirand, Multivariable link invariants arising from Lie superalgebras of type I, J. Knot Theory Ramifications 19 (2010) 93 MR2640994
16 N Geer, B Patureau-Mirand, V Turaev, Modified quantum dimensions and re-normalized link invariants, Compos. Math. 145 (2009) 196 MR2480500
17 N Geer, B Patureau-Mirand, V Turaev, Modified $6j$–symbols and $3$–manifold invariants, Adv. Math. 228 (2011) 1163 MR2822220
18 N Geer, B Patureau-Mirand, A Virelizier, Modified traces and $6j$–symbols in pivotal categories, in preparation
19 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
20 R M Kashaev, Quantum dilogarithm as a $6j$–symbol, Modern Phys. Lett. A 9 (1994) 3757 MR1317945
21 R M Kashaev, A link invariant from quantum dilogarithm, Modern Phys. Lett. A 10 (1995) 1409 MR1341338
22 S Majid, Foundations of quantum group theory, Cambridge Univ. Press (1995) MR1381692
23 H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
24 W D Neumann, Combinatorics of triangulations and the Chern–Simons invariant for hyperbolic $3$–manifolds, from: "Topology '90" (editors B Apanasov, W D Neumann, A W Reid, L Siebenmann), Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 243 MR1184415
25 W D Neumann, Hilbert's $3$rd problem and invariants of $3$–manifolds, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1 (1998) 383 MR1668316
26 J Petit, Decomposition of the Turaev–Viro TQFT arXiv:0903.4512
27 V G Turaev, Quantum invariants of knots and $3$–manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co. (1994) MR1292673
28 V Turaev, Homotopy quantum field theory, EMS Tracts in Mathematics 10, Eur. Math. Soc. (2010) MR2674592
29 V G Turaev, O Y Viro, State sum invariants of $3$–manifolds and quantum $6j$–symbols, Topology 31 (1992) 865 MR1191386
30 V Turaev, H Wenzl, Quantum invariants of $3$–manifolds associated with classical simple Lie algebras, Internat. J. Math. 4 (1993) 323 MR1217386