Hyperbolic Volume Workshop Homepage
● Lecture Note (in processing, Last updated :
22th. Aug. 2007) TEX PDF
● Articles on Volumes
- N.
Abrosimov, M. Godoy, A. Mednykh, On the volume of a spherical
octahedra with symmetries,
Journal of Mathematical Sciences, in print (2008) 14 pp.
- Kazuhiko
Aomoto. Analytic structure of Schl\"{a}fli function, Nagoya Math. J. Vol. 68 (1977), 1-16.
- Francis
Bonahon. A Schl\"{a}fli-type formula for
convex cores of hyperbolic 3-manifolds,
J. Differential Geom. 50, No.1 (1998) 25-58.
- Andrew
M. Brunner, Youn W. Lee, and Norbert J. Wielenberg. Polyhedral groups and graph amalgamation
products, Topology and its Applications
20 (1985) 289-304.
- Marc
Culler. Lifting representations to Covering Groups, Advances in Mathematics 59, 64-70 (1986).
- D.
Derevnin, A. Mednykh, M. Pashkevich On the volume of symmetric tetrahedron, Siberian Matheamtical Journal, Vol.45, No.5, pp.840-848, 2004.
- D.
Derevnin, A. Mednykh. On the volume of spherical Lambert cube, arXiv:math.MG/0212301v1, 2005.
- D.
Derevnin, A. Mednykh. A formula for the volume of a hyperbolic
tetrahedron, Communications of the Moscow
Mathematical Society 60, No.2 (2005) 346-348.
- D.
Derevnin, A. Mednykh, M. Mulazzani. Volumes for twist link cone-manifolds, Bol. Soc. Mat. Mexicana (3) 10 (2004) 129-145.
- D.
Derevnin, A. Mednykh. Volume of hyperbolic
tetrahedron, 2004.
- Damian
Heard. Computation of hyperbolic structures on 3-dimensional orbifolds, Thesis of the University of Melbourne, 2005.
- Hugh
M. Hilden, Maria Teresa Lozano and Jose Maria Montesinos-Amilibia. The Chern-Simons invariants of hyperbolic
manifolds via covering spaces,
Bull. London
Math. Soc. 31 (1999) 354-366.
- Taiyo
Inoue. Organizing volumes of
right-angled hyperbolic polyhedra,
Thesis of the University of Berkeley, 2007.
- Ruth
Kellerhals. On the voluem of hyperbolic polyhedra, Math. Ann. 285, 541-569 (1989).
- A.
Mednykh. Trigonometrical
identities and geometrical inequalities for links and knots.
- A.
Mednykh, M. Pashkevich. Elementary formulas for a hyperbolic
tetrahedron, Siberian Mathematical
Journal, Vol.47, No.4, pp.687-695, 2006.
- A.
Mednykh, C. Petronio. Hyperbolic 3-manifolds with geodesic boundary: Enumeration and
volume calculation, Tr. Mat. Inst. Steklova 252, Geom. Topol., Diskret. Geom. i Teor. Mnozh. (2006) 167-183. arXiv:math/04111141v1,
2007.
- A.
Mednykh, V. Petrov. On spontaneous surgery on knots and links, Pr?opa, Andr? et al., Non-Euclidean geometries. J?os Bolyai
memorial volume. Papers from the international conference on hyperbolic
geometry, Budapest, Hungary, July 6-12, 2002. New York, NY: Springer.
Mathematics and its Applications (Springer) 581, 2006, pp. 307-319.
- Yana
Zilberberg Mohanty. Hyperbolic polyhedra: volume and scissors congruence, thesis, 2002.
- J.
Murakami. Generalized volume and geometric structure
of 3-manifolds, Low-dimensional topology of
tomorrow, No.1272 (2002) 91-113.
- Jessica
S. Purcell. Volumes of highly twisted knots and links, Alebr. Geom. Topol. 7 (2007) 93-108.
- Robert
Riley. Applications of a computer implementation of Poincare's theorem on
fundamental polyhedra, Mathematics of computation,
Vol 40, Num 162, April 1983, 607-632.
- Roland
K. W. Roeder. Constructing hyperbolic polyhedra using Newton's Method, 2006.
- Makoto
Sakuma and Jeffrey R. Weeks. The
generalized Tilt formula, Geometriae Dedicata 55:115-123, 1995.
- Jean-Marc
Schlenker, Rabah Souam. Higher Schl\"{a}fli
formulas and applications, Compositio Mathematica 135: 1-24, 2003.
- Rabah
Souam. The Schl\"{a}fli formula for
polyhedra and piecewise smooth hypersurfaces, Differential Geometry and its Applications 20 (2004) 31-45..
- Gaetano
Sforza, Spazi
metrico-proiettivi, Ricerche di Estensionimetria
differenziale, Serie III, VIII (1906) 3-66.
- A.
Yu. Vesnin. Three-dimensional hyperbolic manifolds with general fundamental
polyhedron, Translated from
Mathematicheskie Zametki, Vol. 49, No.6, 29-32, June, 1991.
- N.
S. Zindinova. Uniformization of some Riemann surfaces with nodes, Siberian Mathematical Journal, Vol. 37, No. 5, 1996.
● Articles on Dilogarithm and Chern-Simons
invariant
- N.
Abrosimov, The Chern-Simons Invariants of Cone-Manifolds with the Whitehead
Link Singular Set, Siberian Advances in
Mathematics Vol 18, No. 2 (2007) 1-9.
- N.
Abrosimov, On Chern-Simons invariants of geometric 3-manifolds, Siberian Electronic Mathematical Reports Vol 3, (2006) 67-70.
- Jinseok
Cho, Lecture Note : Lobachevsky function and dilogarithm function, 2007.
- Anatol
N. Kirillov, Dilogarithm identities,
Arxiv: hep-th/9408113 and Prog.Theor.Phys.Suppl. 118 (1995) 61-142.
- Leonard
C. Maximon, The dilogarithm function for complex argument, Proc. R. Soc. Lond.
A (2003) 459, 2807-2819.
- Walter
D. Nuemann and Don Zagier, Volumes of hyperbolic
three-manifolds, Topology Vol 24, No. 3,
pp.308-332, 1985.
- Walter
D. Neumann, Combinatorics of Triangulations and the Chern-Simons Invariant for
Hyperbolic 3-Manifolds, In "Topology 90",
Walter de Gruyter, 1992, pp. 243-271.
- Walter
D. Nuemann, Hilbert's 3rd Problem and Invariants of
3-manifolds, Geometry and Topology
Monographs, Vol 1: The Epstein Birthday Schrift, 383-411, 1998.
- Walter
D. Nuemann, Extended Block group and the Cheeger-Chern-Simons
class, Geometry and Topology, Vol 8
(2004), 413-474.
- Tomoyoshi
Yoshida, The eta-invariant of hyperbolic 3-manifolds, Invent. Math.
81, 473-514 (1985).
- Don
Zagier, The
Dilogarithm Function, In "Frontiers in Number
Theory, Physics, and Geometry II : On Conformal Field THeories, Discrete
Groups and Renormalization", pp. 3-65, Springer 2007.
● References
- Sangyop
Lee, Dehn fillings on 3-manifolds,
January 27~28, 2008.
- James
W. Cannon, William J. Floyd, Richard Kenyon, and Walter R. Parry, Hyperbolic
Geometry, Flavors of Geometry, MSRI
Publications, Volume 31, 1997.
- N.
Abrosimov, The Seidel problem on the volume of
hyperbolic tetrahedra, presentation at Warwick Symposium
on Low Dimensional Geometry and Topology, July 6, 2007.
- William
Menasco and Morwen Thistlethwaite(ed.), Handbook of knot theory, from ArXiv.
- A.
Marden, Outer Circles : An introduction to hyperbolic 3-manifolds (Book), 2007. From
A. Marden's homepage.
- Damian
Heard, Computation of hyperbolic structure on 3-dimensional orbifolds
(Thesis), 2005.
● Links
If you have any questions or suggestions, please contact Jinseok Cho(jindol@math.snu.ac.kr) or Seonhwa Kim(ryeona17@snu.ac.kr).