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Lectures on Lagrangian torus fibrations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lectures on Lagrangian torus fibrationsJonny Evans, University of Lancaster.
作者:	Evans, Jonny
出版者:	Cambridge, United Kingdom ;Cambridge University Press,2023.
面頁冊數:	xiii, 225 p. :ill., digital ;25 cm.
附註:	Title from publisher's bibliographic system (viewed on 10 Jul 2023).
標題:	Torus (Geometry)
電子資源:	https://doi.org/10.1017/9781009372671
ISBN:	9781009372671

Lectures on Lagrangian torus fibrations
Evans, Jonny(Mathematician)

Lectures on Lagrangian torus fibrations[electronic resource] /Jonny Evans, University of Lancaster. - Cambridge, United Kingdom ;Cambridge University Press,2023. - xiii, 225 p. :ill., digital ;25 cm. - London Mathematical Society student texts ;105. - London Mathematical Society student texts ;81..

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.

ISBN: 9781009372671Subjects--Topical Terms:

347652
Torus (Geometry)

LC Class. No.: QA613.2 / .E93 2023

Dewey Class. No.: 516.158

Lectures on Lagrangian torus fibrations
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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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