Konuslıq kópobrazlıqtıń kólemin kompyuter baǵdarlamalarında esaplaw usılları haqqında

Avtorlar

  • A.B Qutbaev

Gilt sózler: hyperbolic geometry, cone-manifold, orbifold, hyperbolic volume, invariant

Annotaciya

In this work, methods for computing volumes of cone manifolds for knots in hyperbolic geometry are presented, along with differences between computations performed in the computer programs SnapPy and Wolfram Mathematica 13.2.

Paydalanılǵan ádebiyatlar

1. Weeks J., SnapPea: A computer program for creating and studying hyperbolic 3-manifolds, 2001.

2. Culler M., Dunfield N., Goerner M., Jeffrey W. SnapPy, a computer program for studying the geometry and topology of 3-manifolds, Available at http://snappy.computop.org

3. Mednykh A.D., Qutbaev A.B. Hyperbolic Volumes of Two Bridge Cone-Manifolds. // The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 51. – Р. 21-33.

4. Rolfsen D. Knots and Links, AMS, 2003.

5. Porti J. Spherical cone structures on 2-bridge knots and links. // Kobe J. Math., 2004, vol. 21, no. 1-2. – Р. 61-70.

6. Riley R. Seven excellent knots. Low-dimensional Topology, 1982, vol. 48. – P. 81-151.

7. Brin M., Jones G., Singerman D. Commentary on Robert Riley’s article “A personal account of the discovery of hyperbolic structures on some knot complements”. Exp. Math., 2013, vol. 31, no. 2. – P. 99-103.

8. Riley R. A personal account of the discovery of hyperbolic structure on some knot complements. Exp. Math., 2013, vol. 31, no. 2. – P. 104-115.