Příčné uzly
| Thesis title in Czech: | Příčné uzly |
|---|---|
| Thesis title in English: | Transverse knots |
| Key words: | Contact vector space, transverse knot, transverse Reidemeister moves, classical invariants of transverse knots |
| English key words: | Contact vector space, transverse knot, transverse Reidemeister moves, classical invariants of transverse knots |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | Roman Golovko, Ph.D. |
| Author: |
| Guidelines |
| (1) The notion of contact vector space
(2) The notion of transverse knot (3) Transverse isotopies and transverse Reidemeister moves (4) Classical invariants of transverse knots |
| References |
| J. B. Etnyre, Legendrian and transversal knots, Handbook of knot theory, Elsevier B. V., Amsterdam, 2005, pp. 105–185.
H. Geiges, An introduction to contact topology; Volume 109 of Cambridge studies in advanced mathematics. Cambridge University Press. 2008 |
| Preliminary scope of work |
| Contact structures on manifolds and transversal knots in them are very natural objects, born over two centuries ago, in the work of Huygens, Hamilton and Jacobi on geometric optics and work of Lie on partial differential equations. They touch on diverse areas of mathematics and physics, and have deep connections with topology and dynamics in low dimensions. |
| Preliminary scope of work in English |
| Contact structures on manifolds and transversal knots in them are very natural objects, born over two centuries ago, in the work of Huygens,Hamilton and Jacobi on geometric optics and work of Lie on partial differential equations. They touch on diverse areas of mathematics and physics, and have deep connections with topology and dynamics in low dimensions. |