{"product_id":"9789814725507","title":"Representing 3-manifolds By Filling Dehn Surfaces","description":"\u003cp\u003eThis book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects.\u003c\/p\u003e\u003cp\u003e\u003ci\u003eRepresenting 3-Manifolds by Filling Dehn Surfaces\u003c\/i\u003e is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.\u003c\/p\u003e\u003cbr\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003ePreliminaries:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eSets\u003c\/li\u003e\n\u003cli\u003eManifolds\u003c\/li\u003e\n\u003cli\u003eCurves\u003c\/li\u003e\n\u003cli\u003eTransversality\u003c\/li\u003e\n\u003cli\u003eRegular deformations\u003c\/li\u003e\n\u003cli\u003eComplexes\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eFilling Dehn Surfaces:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eDehn Surfaces in 3-manifolds\u003c\/li\u003e\n\u003cli\u003eFilling Dehn Surfaces\u003c\/li\u003e\n\u003cli\u003eNotation\u003c\/li\u003e\n\u003cli\u003eSurgery on Dehn Surfaces. Montesinos Theorem\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eJohansson Diagrams:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eDiagrams Associated to Dehn Surfaces\u003c\/li\u003e\n\u003cli\u003eAbstract Diagrams on Surfaces\u003c\/li\u003e\n\u003cli\u003eThe Johansson Theorem\u003c\/li\u003e\n\u003cli\u003eFilling Diagrams\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eFundamental Group of a Dehn Sphere:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eCoverings of Dehn Spheres\u003c\/li\u003e\n\u003cli\u003eThe Diagram Group\u003c\/li\u003e\n\u003cli\u003eCoverings and Representations\u003c\/li\u003e\n\u003cli\u003eApplications\u003c\/li\u003e\n\u003cli\u003eThe Fundamental Group of a Dehn \u003ci\u003eg\u003c\/i\u003e-torus\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eFilling Homotopies:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eFilling Homotopies\u003c\/li\u003e\n\u003cli\u003eBad Haken Moves\u003c\/li\u003e\n\u003cli\u003e\"Not so Bad\" Haken Moves\u003c\/li\u003e\n\u003cli\u003eDiagram Moves\u003c\/li\u003e\n\u003cli\u003eDuplication\u003c\/li\u003e\n\u003cli\u003eAmendola's Moves\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eProof of Theorem 5.8:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003ePushing Disks\u003c\/li\u003e\n\u003cli\u003eShellings. Smooth Triangulations\u003c\/li\u003e\n\u003cli\u003eComplex \u003ci\u003e\u003cb\u003ef\u003c\/b\u003e\u003c\/i\u003e-moves\u003c\/li\u003e\n\u003cli\u003eInflating Triangulations\u003c\/li\u003e\n\u003cli\u003eFilling Pairs\u003c\/li\u003e\n\u003cli\u003eSimultaneous Growings\u003c\/li\u003e\n\u003cli\u003eProof of Theorem 5.8\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003ci\u003e\u003cb\u003eThe Triple Point Spectrum:\u003c\/b\u003e\u003c\/i\u003e\u003cul\u003e\n\u003cli\u003eThe Shima's Spheres\u003c\/li\u003e\n\u003cli\u003eSome Examples of Filling Dehn Surfaces\u003c\/li\u003e\n\u003cli\u003eThe Number of Triple Points as a Measure of Complexity: Montestinos Complexity\u003c\/li\u003e\n\u003cli\u003eThe Triple Point Spectrum\u003c\/li\u003e\n\u003cli\u003eSurface-complexity\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eKnots, Knots and Some Open Questions:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e2-Knots: Lifting Filling Dehn Surfaces\u003c\/li\u003e\n\u003cli\u003e1-Knots\u003c\/li\u003e\n\u003cli\u003eOpen Problems\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Graduate students and researchers interested in low-dimensional topology.\u003cbr\u003e3-Manifolds;Immersed Surfaces;Dehn Surfaces;Johansson Diagrams;Set of Moves;Regular Homotopies\u003cb\u003eKey Features:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIt provides deep results in a new subject of mathematical research. Moreover, it introduces new mathematical tools and techniques useful in different areas of low-dimensional topology\u003c\/li\u003e\n\u003cli\u003eThe book uses topological and combinatorial tools developed all along the twentieth century making the volume a trip along the history of low-dimensional topology\u003c\/li\u003e\n\u003cli\u003eA spectacular set of pictures, in the better tradition of low-dimensional topology books, which give deep insight of the techniques and constructions done in the book\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47185440997616,"sku":"9789814725507","price":63.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814725507_p0.jpg?v=1763692798","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814725507","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}