Lectures on Lagrangian Torus Fibrations

Jonny Evans

ISBN 10: 1009372629 / ISBN 13: 9781009372626

Editore: Cambridge University Press, 2023

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243 pages. 9.00x6.00x0.69 inches. In Stock. This item is printed on demand.

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Dati bibliografici

• Titolo: Lectures on Lagrangian Torus Fibrations
• Editore: Cambridge University Press
• Data di pubblicazione: 2023
• Lingua: Inglese
• ISBN 10: 1009372629
• ISBN 13: 9781009372626
• Rilegatura: Hardcover
• Condizione: Brand New
• Peso: 0,52 chilogrammi

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Riassunto

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.