Lectures on Lagrangian torus fibrations:
Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and ma...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge, United Kingdom
Cambridge University Press
2023
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| Series: | London Mathematical Society student texts
105 |
| Subjects: | |
| Online Access: | BSB01 BTU01 FHN01 Volltext |
| Summary: | Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry |
| Item Description: | Title from publisher's bibliographic system (viewed on 10 Jul 2023) |
| Physical Description: | 1 Online-Ressource (xiii, 225 Seiten) |
| ISBN: | 9781009372671 |
| DOI: | 10.1017/9781009372671 |
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| 520 | |a Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry | ||
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| isbn | 9781009372671 |
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| spelling | Evans, Jonny (Mathematician) aut Lectures on Lagrangian torus fibrations Jonny Evans, University of Lancaster Cambridge, United Kingdom Cambridge University Press 2023 1 Online-Ressource (xiii, 225 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 105 Title from publisher's bibliographic system (viewed on 10 Jul 2023) Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry Torus (Geometry) Symplectic manifolds Symplectic geometry Erscheint auch als Druck-Ausgabe 978-1-009-37263-3 Erscheint auch als Druck-Ausgabe 978-1-009-37262-6 https://doi.org/10.1017/9781009372671 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Evans, Jonny (Mathematician) Lectures on Lagrangian torus fibrations Torus (Geometry) Symplectic manifolds Symplectic geometry |
| title | Lectures on Lagrangian torus fibrations |
| title_auth | Lectures on Lagrangian torus fibrations |
| title_exact_search | Lectures on Lagrangian torus fibrations |
| title_exact_search_txtP | Lectures on Lagrangian torus fibrations |
| title_full | Lectures on Lagrangian torus fibrations Jonny Evans, University of Lancaster |
| title_fullStr | Lectures on Lagrangian torus fibrations Jonny Evans, University of Lancaster |
| title_full_unstemmed | Lectures on Lagrangian torus fibrations Jonny Evans, University of Lancaster |
| title_short | Lectures on Lagrangian torus fibrations |
| title_sort | lectures on lagrangian torus fibrations |
| topic | Torus (Geometry) Symplectic manifolds Symplectic geometry |
| topic_facet | Torus (Geometry) Symplectic manifolds Symplectic geometry |
| url | https://doi.org/10.1017/9781009372671 |
| work_keys_str_mv | AT evansjonny lecturesonlagrangiantorusfibrations |