Ji-Young Ham

The Minimum Dilatation of Pseudo-Anosov 5-Braids

The minimum dilatation of pseudo-Anosov 5-braids is shown to be the largest zero λ5 ≈ 1.72208 of x 4 -x 3 -x 2 -x+1, which is attained by σ1σ2σ3σ4σ1σ2.

The Minimal Dilatation of a Genus-Two Surface

We show that the minimal dilatation of pseudo-Anosov homeomorphisms of a closed oriented genus-two surface is equal to the largest root of x 4 – x 3 – x 2 – x + 1, which is approximately 1.72208.

An explicit formula for the A-polynomial of the knot with Conway’s notation C(2n,3)

An explicit formula for the

Явные формулы для инвариантов Черна - Саймонса орбиобразий скрученных узлов и реберные многочлены скрученных узлов@@@Explicit formulae for Chern-Simons invariants of the twist-knot orbifolds and edge polynomials of twist knots

A

On the volume and Chern–Simons invariant for 2-bridge knot orbifolds

-polynomial of the knot with Conways notation

Trigonometric identities and volumes of the hyperbolic twist knot cone-manifolds

C(2n,3)

The volume of hyperbolic cone-manifolds of the knot with Conway’s notation C(2n,3)

is obtained from the explicit Riley-Mednykh polynomial of it.

Explicit formulae for Chern-Simons invariants of the twist-knot orbifolds and edge polynomials of twist knots

[1] Shiing-Shen Chern, J. Simons, “Some cohomology classes in principal fiber bundles and their application to Riemannian geometry”, Proc. Nat. Acad. Sci. U.S.A., 68:4 (1971), 791–794 MathSciNet Zentralblatt MATH [2] R. Meyerhoff, “Hyperbolic 3-manifolds with equal volumes but different Chern– Simons invariants”, Low-dimensional topology and Kleinian groups (Coventry/ Durham, 1984), London Math. Soc. Lecture Note Ser., 112, Cambridge Univ. Press, Cambridge, 1986, 209–215 MathSciNet Zentralblatt MATH [3] W.D. Neumann, “Combinatorics of triangulations and the Chern–Simons invariant for hyperbolic 3-manifolds”, Topology ’90 (Columbus, OH, 1990), Ohio State Univ. Math. Res. Inst. Publ., 1, de Gruyter, Berlin, 1992, 243–271 MathSciNet Zentralblatt MATH [4] W.D. Neumann, “Extended Bloch group and the Cheeger–Chern–Simons class”, Geom. Topol., 8 (2004), 413–474 MathSciNet Zentralblatt MATH [5] Ch.K. Zickert, “The volume and Chern–Simons invariant of a representation”, Duke Math. J., 150:3 (2009), 489–532 MathSciNet Zentralblatt MATH [6] J. Cho, J. Murakami, Y. Yokota, “The complex volumes of twist knots”, Proc. Amer. Math. Soc., 137:10 (2009), 3533–3541 MathSciNet Zentralblatt MATH [7] J. Cho, J. Murakami, “The complex volumes of twist knots via colored Jones polynomials”, J. Knot Theory Ramifications, 19, no. 11, 1401–1421 MathSciNet Zentralblatt MATH

Explicit formulae for Chern–Simons invariants of the hyperbolic orbifolds of the knot with Conway’s notation C(2n, 3)

This paper extends the work by Mednykh and Rasskazov presented in [On the structure of the canonical fundamental set for the 2-bridge link orbifolds, Universitat Bielefeld, Sonderforschungsbereich 343, Discrete Structuren in der Mathematik, Preprint (1988), pp. 98–062, www.mathematik.uni-bielefeld.de/sfb343/preprints/pr98062.ps.gz]. By using their approach, we derive the Riley–Mednykh polynomial for a family of 2-bridge knot orbifolds. As a result, we obtain explicit formulae for the volumes and Chern–Simons invariants of orbifolds and cone-manifolds on the knot with Conway’s notation C(2n, 4).