{"product_id":"convex-integration-theory-solutions-to-the-h-principle-in-geometry-and-topology-9783764358051","title":"Convex Integration Theory: Solutions to the H-Principle in Geometry and Topology","description":"\u003cp\u003e • Author(s): David Spring\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Topology - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e1. Historical Remarks Convex Integration theory, first introduced by M. Gromov [17], is one of three general methods in immersion-theoretic topology for solving a broad range of problems in geometry and topology. The other methods are: (i) Removal of Singularities, introduced by M. Gromov and Y. Eliashberg [8]; (ii) the covering homotopy method which, following M. Gromov's thesis [16], is also referred to as the method of sheaves. The covering homotopy method is due originally to S. Smale [36] who proved a crucial covering homotopy result in order to solve the classification problem for immersions of spheres in Euclidean space. These general methods are not linearly related in the sense that succes- sive methods subsumed the previous methods. Each method has its own distinct foundation, based on an independent geometrical or analytical insight. Conse- quently, each method has a range of applications to problems in topology that are best suited to its particular insight. For example, a distinguishing feature of Convex Integration theory is that it applies to solve closed relations in jet spaces, including certain general classes of underdetermined non-linear systems of par- tial differential equations. As a case of interest, the Nash-Kuiper Cl-isometrie immersion theorem ean be reformulated and proved using Convex Integration theory (cf. Gromov [18]). No such results on closed relations in jet spaees can be proved by means of the other two methods.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45283252535447,"sku":"9783764358051","price":7345.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783764358051.webp?v=1769304491","url":"https:\/\/atlanticbooks.com\/products\/convex-integration-theory-solutions-to-the-h-principle-in-geometry-and-topology-9783764358051","provider":"Atlantic Books","version":"1.0","type":"link"}