{"product_id":"lectures-on-seiberg-witten-invariants-john-d-moore-9783540412212","title":"Lectures on Seiberg-Witten Invariants","description":"Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa- tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang- Mills connections. For studying such equations, a new unified technology has been developed, involving analysis on infinite-dimensional manifolds. A striking applications of the new technology is Donaldson's theory of \"anti-self-dual\" connections on SU(2)-bundles over four-manifolds, which applies the Yang-Mills equations from mathematical physics to shed light on the relationship between the classification of topological and smooth four-manifolds. This reverses the expected direction of application from topology to differential equations to mathematical physics. Even though the Yang-Mills equations are only mildly nonlinear, a prodigious amount of nonlinear analysis is necessary to fully understand the properties of the space of solutions. . At our present state of knowledge, understanding smooth structures on topological four-manifolds seems to require nonlinear as opposed to linear PDE's. It is therefore quite surprising that there is a set of PDE's which are even less nonlinear than the Yang-Mills equation, but can yield many of the most important results from Donaldson's theory. These are the Seiberg-Witte equations. These lecture notes stem from a graduate course given at the University of California in Santa Barbara during the spring quarter of 1995. The objective was to make the Seiberg-Witten approach to Donaldson theory accessible to second-year graduate students who had already taken basic courses in differential geometry and algebraic topology.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e John D. Moore\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3540412212\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783540412212\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 04\/24\/2001\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 121\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.44lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.29d","brand":"John D. Moore","offers":[{"title":"Paperback","offer_id":44159459852543,"sku":"9783540412212","price":44.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_0ebe7ff2-4604-427c-9822-9175b1291896.jpg?v=1689082735","url":"https:\/\/www.whiterainbookhouse.com\/products\/lectures-on-seiberg-witten-invariants-john-d-moore-9783540412212","provider":"WR Book House","version":"1.0","type":"link"}