Geometry & Topology Volume 9, issue 1 (2005)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Classical and quantum dilogarithmic invariants of flat $PSL(2,\mathbb{C})$–bundles over 3–manifolds

Stephane Baseilhac and Riccardo Benedetti

Geometry & Topology 9 (2005) 493–569

DOI: 10.2140/gt.2005.9.493

Bibliography

1	S Baseilhac, Dilogarithme Quantique et Invariants de 3–Variétés, PhD thesis, Université Paul Sabatier, Toulouse (2001)
2	S Baseilhac, R Benedetti, QHI, 3–manifolds scissors congruence classes and the volume conjecture, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 13 MR2002600
3	S Baseilhac, R Benedetti, Quantum hyperbolic invariants of 3–manifolds with $\mathrm{PSL}(2,\mathbb{C})$–characters, Topology 43 (2004) 1373 MR2081430
4	S Baseilhac, R Benedetti, 3D quantum hyperbolic field theory arXiv:math.GT/0409282
5	R Benedetti, C Petronio, Lectures on hyperbolic geometry, Universitext, Springer (1992) MR1219310
6	R Benedetti, C Petronio, Branched standard spines of 3–manifolds, Lecture Notes in Mathematics 1653, Springer (1997) MR1470454
7	V V Bazhanov, N Y Reshetikhin, Remarks on the quantum dilogarithm, J. Phys. A 28 (1995) 2217 MR1338071
8	S Baaj, G Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de $C^$–algèbres*, Ann. Sci. École Norm. Sup. $(4)$ 26 (1993) 425 MR1235438
9	B G Casler, An imbedding theorem for connected 3–manifolds with boundary, Proc. Amer. Math. Soc. 16 (1965) 559 MR0178473
10	F Costantino, A calculus for branched spines of 3–manifolds, Math. Z. 251 (2005) 427 MR2191035
11	V Chari, A Pressley, A guide to quantum groups, Cambridge University Press (1994) MR1300632
12	A A Davydov, Pentagon equation and matrix bialgebras, Comm. Algebra 29 (2001) 2627 MR1845134
13	N M Dunfield, Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds, Invent. Math. 136 (1999) 623 MR1695208
14	J L Dupont, C H Sah, Scissors congruences II, J. Pure Appl. Algebra 25 (1982) 159 MR662760
15	J L Dupont, The dilogarithm as a characteristic class for flat bundles, from: "Proceedings of the Northwestern conference on cohomology of groups (Evanston, Ill., 1985)" (1987) 137 MR885101
16	J L Dupont, Scissors congruences, group homology and characteristic classes, Nankai Tracts in Mathematics 1, World Scientific Publishing Co. (2001) MR1832859
17	D B A Epstein, R C Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988) 67 MR918457
18	L D Faddeev, R M Kashaev, Quantum dilogarithm, Modern Phys. Lett. A 9 (1994) 427 MR1264393
19	S Francaviglia, Hyperbolic volume of representations of fundamental groups of cusped 3–manifolds, Int. Math. Res. Not. (2004) 425 MR2040346
20	R M Kashaev, A link invariant from quantum dilogarithm, Modern Phys. Lett. A 10 (1995) 1409 MR1341338
21	R M Kashaev, The algebraic nature of quantum dilogarithm, from: "Geometry and integrable models (Dubna, 1994)", World Sci. Publ., River Edge, NJ (1996) 32 MR1413505
22	R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269 MR1434238
23	C Kassel, Quantum groups, Graduate Texts in Mathematics 155, Springer (1995) MR1321145
24	L Lewin, Dilogarithms and associated functions, Foreword by J. C. P. Miller, Macdonald, London (1958) MR0105524
25	S V Matveev, Transformations of special spines, and the Zeeman conjecture, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987) 1104, 1119 MR925096
26	R Meyerhoff, Hyperbolic 3–manifolds with equal volumes but different Chern–Simons invariants, from: "Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984)", London Math. Soc. Lecture Note Ser. 112, Cambridge Univ. Press (1986) 209 MR903866
27	H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
28	W D Neumann, Combinatorics of triangulations and the Chern–Simons invariant for hyperbolic 3–manifolds, from: "Topology '90 (Columbus, OH, 1990)", Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 243 MR1184415
29	W D Neumann, Hilbert's 3rd problem and invariants of 3–manifolds, from: "The Epstein birthday schrift", Geom. Topol. Monogr. 1, Geom. Topol. Publ., Coventry (1998) 383 MR1668316
30	W D Neumann, Extended Bloch group and the Chern–Simons class, incomplete working version arXiv:math.GT/0212147
31	W D Neumann, Extended Bloch group and the Cheeger–Chern–Simons class, Geom. Topol. 8 (2004) 413 MR2033484
32	W D Neumann, J Yang, Bloch invariants of hyperbolic 3–manifolds, Duke Math. J. 96 (1999) 29 MR1663915
33	W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
34	T Ohtsuki, T Kohno, T Le, J Murakami, J Roberts, V Turaev, Invariants of knots and 3–manifolds, Geometry & Topology Monographs 4, Geometry & Topology Publications, Coventry (2002) MR2000786
35	R Piergallini, Standard moves for standard polyhedra and spines, Rend. Circ. Mat. Palermo $(2)$ Suppl. (1988) 391 MR958750
36	M A Semenov-Tian-Shansky, Poisson Lie groups, quantum duality principle, and the quantum double, from: "Mathematical aspects of conformal and topological field theories and quantum groups (South Hadley, MA, 1992)", Contemp. Math. 175, Amer. Math. Soc. (1994) 219 MR1302020
37	V G Turaev, Quantum invariants of knots and 3–manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co. (1994) MR1292673
38	D Zagier, The remarkable dilogarithm, J. Math. Phys. Sci. 22 (1988) 131 MR940391