{"product_id":"the-seiberg-witten-equations-and-applications-to-the-topology-of-smooth-four-manifolds-mn-44-volume-44-paperback","title":"The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (Mn-44), Volume 44 - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eJohn W. Morgan\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e The work begins with a review of the classical material on Spin \u003ci\u003ec\u003c\/i\u003e structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003eBeginning with the groundbreaking work of Donaldson in about 1980 it became clear that gauge-theoretic invariants of principal bundles and connections were an important tool in the study of smooth four-dimensional manifolds. Donaldson showed the importance of the moduli space of antiself-dual connections. The next fifteen years saw an explosion of work in this area leading to computations of Donaldson polynomial invariants for a wide class of four-dimensional manifolds, especially algebraic surfaces.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eJohn W. Morgan\u003c\/b\u003e is Professor of Mathematics at Columbia University.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 130\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.46 x 9.25 x 6.16 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e December 31, 1995\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":48261342789853,"sku":"9780691025971","price":162.11,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0811\/9867\/8237\/files\/fq3bh-xK3t9780691025971.webp?v=1785074023","url":"https:\/\/handfulofbooks.com\/products\/the-seiberg-witten-equations-and-applications-to-the-topology-of-smooth-four-manifolds-mn-44-volume-44-paperback","provider":"Handful of Books","version":"1.0","type":"link"}