Kvantitativní aspekty Legenreových podvariet
| Thesis title in Czech: | Kvantitativní aspekty Legenreových podvariet |
|---|---|
| Thesis title in English: | Quantitative aspects of Legendrian submanifolds |
| Key words: | kontaktní topologie|Legenreovy podvariety|Arnoldova domněnka|augmentace |
| English key words: | contact topology|Legendrian submanifolds|Arnold's conjecture|augmentions |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | Roman Golovko, Ph.D. |
| Author: |
| Guidelines |
| The thesis aims to investigate the quantitative aspects of contact topology related to Legendrian submanifolds and Lagrangian cobordisms between them. Among the questions to study there are the numerical aspects of Arnold's conjecture under various geometric restrictions, the size of Lagrangian cobordisms and the numerical analysis of augmentations.
Hlavním cílem je studovat kvantitativní aspekty kontaktní topologie související s Legenreovými subvarietami a Lagrangeovými kobordismy mezi nimi. Mezi otázky ke studiu patří numerické aspekty Arnoldovy domněnky pod různými geometrickými omezeními, velikost Lagrangových kobordismů a numerická analýza augmentací. |
| References |
| B. Chantraine, G. Dimitroglou Rizell, P. Ghiggini and R. Golovko, Floer theory for Lagrangian cobordisms,
Journal of Differential Geometry, Volume 114, Number 3 (2020), 393-465. G. Dimitroglou Rizell and R. Golovko, The stable Morse number as a lower bound for the number of Reeb chords, Journal of Symplectic Geometry, Vol. 16, No. 5 (2018), 1209-1248. T. Ekholm and J. Etnyre and M. Sullivan, The contact homology of Legendrian submanifolds in R2n+1, J. Differential Geom. 71 (2005), no. 2, 177–305. Y. Eliashberg, A. Givental and H. Hofer, Introduction to symplectic field theory, GAFA 2000 (Tel Aviv, 1999), Geom. Funct. Anal. 2000, Special Volume, Part II, 560–673. J. Sabloff and L. Traynor, The minimal length of a Lagrangian cobordism between Legendrians Selecta Mathematica, Volume 23, pages 1419–1448, (2017). |