Floer Homology Groups in Yang-Mills Theory (Cambridge Tracts in Mathematics)

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9780521808033: Floer Homology Groups in Yang-Mills Theory (Cambridge Tracts in Mathematics)
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This monograph gives a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The material contained here was developed with specific applications in mind. However, it has now become clear that the techniques used are important for many current areas of research. An important example would be symplectic theory and gluing problems for self-dual metrics and other metrics with special holonomy. The author writes with the big picture constantly in mind. As well as a review of the current state of knowledge, there are sections on the likely direction of future research. Included in this are connections between Floer groups and the celebrated Seiberg-Witten invariants. The results described in this volume form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution.

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This monograph aims to give a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The techniques used here are now known to be important for many current areas of research. The author writes with the big picture constantly in mind, reviewing the current state of knowledge and predicting the likely direction of future research. The results described form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution.

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"This book gives a thorough and extensive treatment...this text is a wonderfully written exposition of Floer homology which no mathematics library should be without." Mathematical Reviews

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2010. Hardback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****. The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer s construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject. Seller Inventory # APC9780521808033

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2010. Hardback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****.The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer s construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject. Seller Inventory # APC9780521808033

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