Reprezentace Chekanovových-Eliashbergových algeber
| Thesis title in Czech: | Reprezentace Chekanovových-Eliashbergových algeber |
|---|---|
| Thesis title in English: | On representations of Chekanov-Eliashberg algebras |
| Key words: | reprezentace, Chekanovova-Eliashbergova algebra, Legendréovy podvariety |
| English key words: | representation, Chekanov-Eliashberg algebra, Legendrian submanifold |
| Academic year of topic announcement: | 2018/2019 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | doc. Roman Golovko, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 12.06.2019 |
| Date of assignment: | 13.06.2019 |
| Confirmed by Study dept. on: | 05.06.2020 |
| Date and time of defence: | 09.07.2020 10:00 |
| Date of electronic submission: | 24.05.2020 |
| Date of submission of printed version: | 28.05.2020 |
| Date of proceeded defence: | 09.07.2020 |
| Opponents: | Hong Van Le, Ph.D. |
| Guidelines |
| Student nastuduje základy teorie Legendréových podvariet kontaktních varier. Hlavním cílem je naučit se klasické a moderní invarianty v této teorii, zkoumat
a konstruovat reprezentace Chekanovových--Eliashbergových algeber pro specifické Legendréovy uzly. The student will study the basics of the theory of Legendrian submanifolds of a contact manifold. The main goal is to learn about the classical and modern invariants in this theory, in particular to investigate and construct some representations of Chekanov--Eliashberg algebras of certain Legendrian knots. |
| References |
| S. Sivek, The contact homology of Legendrian knots with maximal Thurston-Bennequin invariant, J. Symplectic Geom. 11 (2013), no. 2, 167-178
L. Ng and D. Rutherford, Satellites of Legendrian knots and representations of the Chekanov-Eliashberg algebra, Algebr. Geom. Topol. 13 (2013) 3047-3097 G. Dimitroglou Rizell and R. Golovko, Estimating the number of Reeb chords using a linear representation of the characteristic algebra, Algebr. Geom. Topol. 15 (2015) 2887-2920 C. Leverson and D. Rutherford, Satellite ruling polynomials, DGA representations, and the colored HOMFLY-PT polynomial, preprint 2018, arxiv:1802.10531 B. Chantraine, L. Ng and S. Sivek, Representations, sheaves, and Legendrian (2,m)-torus links, preprint 2018, arXiv:1805.03603 L. Ng and J. Etnyre, Legendrian contact homology in R^3, preprint 2018, arXiv:1811.10966 |