Legendrovské uzly
| Thesis title in Czech: | Legendrovské uzly |
|---|---|
| Thesis title in English: | Legendrian knots |
| Key words: | Contact vector space, Legendrian knot, Legendrian isotopies and Legendrian Reidemeister moves, classical invariants of Legendrian knots |
| English key words: | Contact vector space, Legendrian knot, Legendrian isotopies and Legendrian Reidemeister moves, classical invariants of Legendrian 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 Legendrian knot (3) Legendrian isotopies and Legendrian Reidemeister moves (4) Legendrian approximation (5) Classical invariants of Legendrian 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 Legendrian 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 Legendrian 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 |