{"product_id":"lectures-on-lagrangian-torus-fibrations-paperback-9781009372633","title":"Lectures on Lagrangian Torus Fibrations (Paperback) 9781009372633","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLectures on Lagrangian Torus Fibrations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eComprehensive and visual introduction to the geometry of 4-dimensional symplectic manifolds via 2-dimensional almost-toric diagrams.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJonny Evans (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009372633, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 31 July 2023\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e243 pages\u003cbr\u003e27 x 18 x 1.6 cm, 0.415 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This is a lucid and engaging introduction to the fascinating world of (almost) toric geometry, in which one can understand the properties of Lagrangian and symplectic submanifolds in four dimensions simply by drawing suitable two-dimensional diagrams. The book has many illustrations and intricate examples.' Dusa McDuff, Barnard College, Columbia University\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eSymington'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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. The Arnold–Liouville theorem\u003cbr\u003e 2. Lagrangian fibrations\u003cbr\u003e 3. Global action-angle coordinates and torus actions\u003cbr\u003e 4. Symplectic reduction\u003cbr\u003e 5. Visible Lagrangian submanifolds\u003cbr\u003e 6. Focus-focus singularities\u003cbr\u003e 7. Examples of focus-focus systems\u003cbr\u003e 8. Almost toric manifolds\u003cbr\u003e 9. Surgery\u003cbr\u003e 10. Elliptic and cusp singularities\u003cbr\u003e A. Symplectic linear algebra\u003cbr\u003e B. Lie derivatives\u003cbr\u003e C. Complex projective spaces\u003cbr\u003e D. Cotangent bundles\u003cbr\u003e E. Moser's argument\u003cbr\u003e F. Toric varieties revisited\u003cbr\u003e G. Visible contact hypersurfaces and Reeb flows\u003cbr\u003e H. Tropical Lagrangian submanifolds\u003cbr\u003e I. Markov triples\u003cbr\u003e J. Open problems\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Geometry [\u003ca title=\"See our other books on Geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Geometry%20%5BPBM%5D%22\"\u003ePBM\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265432736024,"sku":"9781009372633","price":26.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781009372633i.jpg?v=1692022843","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/lectures-on-lagrangian-torus-fibrations-paperback-9781009372633","provider":"Freshly Printed Books","version":"1.0","type":"link"}