國立虎尾科技大學 |

Lectures on Lagrangian torus fibrations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Lectures on Lagrangian torus fibrations/ Jonny Evans, University of Lancaster.
Author:	Evans, Jonny
Published:	Cambridge, United Kingdom ;Cambridge University Press, : 2023.,
Description:	xiii, 225 p. :ill., digital ; : 25 cm.;
Notes:	Title from publisher's bibliographic system (viewed on 10 Jul 2023).
Subject:	Torus (Geometry) -
Online resource:	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:

895401
Torus (Geometry)

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

Dewey Class. No.: 516.158

Lectures on Lagrangian torus fibrations
LDR:02032nam a2200277 a 4500 001 1138014
003 UkCbUP
005 20230710022011.0
006 m d
007 cr nn 008maaau
008 250110s2023 enk o 1 0 eng d
020 $a 9781009372671 $q (electronic bk.)
020 $a 9781009372626 $q (hardback)
020 $a 9781009372633 $q (paperback)
035 $a CR9781009372671
040 $a UkCbUP $b eng $c UkCbUP $d GP
041 0 $a eng
050 0 0 $a QA613.2 $b .E93 2023
082 0 4 $a 516.158 $2 23
090 $a QA613.2 $b .E92 2023
100 1 $a Evans, Jonny $c (Mathematician) $3 1461559
245 1 0 $a Lectures on Lagrangian torus fibrations $h [electronic resource] / $c Jonny Evans, University of Lancaster.
260 $a Cambridge, United Kingdom ; $a New York, NY : $b Cambridge University Press, $c 2023.
300 $a xiii, 225 p. : $b ill., digital ; $c 25 cm.
490 1 $a London Mathematical Society student texts ; $v 105
500 $a Title from publisher's bibliographic system (viewed on 10 Jul 2023).
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.
650 0 $a Torus (Geometry) $3 895401
650 0 $a Symplectic manifolds. $3 1132461
650 0 $a Symplectic geometry. $3 672649
830 0 $a London Mathematical Society student texts ; $v 81. $3 1156767
856 4 0 $u https://doi.org/10.1017/9781009372671