Lectures on Lagrangian Torus Fibrations (Paperback)

Jonny Evans

ISBN 10: 1009372637 / ISBN 13: 9781009372633

Editore: Cambridge University Press, Cambridge, 2023

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Paperback. 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. This book explains how to use simple 2-dimensional pictures to understand the geometry and topology of 4-dimensional spaces. These spaces are of relevance in Hamiltonian dynamics, in algebraic geometry, and in mathematical string theory. It is suitable for graduate students and researchers in geometry and topology. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9781009372633

Dati bibliografici

• Titolo: Lectures on Lagrangian Torus Fibrations (Paperback)
• Editore: Cambridge University Press, Cambridge
• Data di pubblicazione: 2023
• Lingua: Inglese
• ISBN 10: 1009372637
• ISBN 13: 9781009372633
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

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.