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Lectures on Lagrangian torus fibrations /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Lectures on Lagrangian torus fibrations // Jonny Evans, University of Lancaster.
作者:	Evans, Jonny
面頁冊數:	1 online resource (xiii, 225 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 10 Jul 2023).
標題:	Symplectic geometry. -
電子資源:	https://doi.org/10.1017/9781009372671
ISBN:	9781009372671 (ebook)

Lectures on Lagrangian torus fibrations /
Evans, Jonny(Mathematician),

Lectures on Lagrangian torus fibrations /Jonny Evans, University of Lancaster. - 1 online resource (xiii, 225 pages) :digital, PDF file(s). - 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: 9781009372671 (ebook)Subjects--Topical Terms:

672649
Symplectic 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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