The Geometry of Four-Manifolds (Oxford Mathematical Monographs)

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9780198502692: The Geometry of Four-Manifolds (Oxford Mathematical Monographs)

Book by Donaldson S K Kronheimer P B

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... authoritative and comprehensive... it must be regarded as compulsory reading for any young researcher approaching this difficult but fascinating area. ( Bulletin of the London Mathematical Society)

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This book provides the first lucid and accessible account to the modern study of the geometry of four-manifolds. It has become required reading for postgraduates and research workers whose research touches on this topic. Pre-requisites are a firm grounding in differential topology, and geometry as may be gained from the first year of a graduate course. The subject matter of this book is the most significant breakthrough in mathematics of the last fifty years, and Professor Donaldson won a Fields medal for his work in the area. The authors start from the standpoint that the fundamental group and intersection form of a four-manifold provides information about its homology and characteristic classes, but little of its differential topology. It turns out that the classification up to diffeomorphism of four-manifolds is very different from the classification of unimodular forms and that the study of this question leads naturally to the new Donaldson invariants of four-manifolds. A central theme of this book is that the appropriate geometrical tools for investigating these questions come from mathematical physics: the Yang-Mills theory and anti-self dual connections over four-manifolds. One of the many consequences of this theory is that 'exotic' smooth manifolds exist which are homeomorphic but not diffeomorphic to 4, and that large classes of forms cannot be realized as intersection forms whereas distinct manifolds may share the same form. These results have had far-reaching consequences in algebraic geometry, topology, and mathematical physics, and will continue to be a mainspring of mathematical research for years to come.

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1.

Kronheimer Donaldson, Research Fellow P B Kronheimer, Professor of Mathematics S K Donaldson
Editorial: Oxford University Press, United Kingdom (1997)
ISBN 10: 0198502699 ISBN 13: 9780198502692
Nuevos Paperback Cantidad: 10
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Descripción Oxford University Press, United Kingdom, 1997. Paperback. Estado de conservación: New. Revised ed.. 244 x 170 mm. Language: English . Brand New Book ***** Print on Demand *****.This book provides the first lucid and accessible account to the modern study of the geometry of four-manifolds. It has become required reading for postgraduates and research workers whose research touches on this topic. Pre-requisites are a firm grounding in differential topology, and geometry as may be gained from the first year of a graduate course. The subject matter of this book is the most significant breakthrough in mathematics of the last fifty years, and Professor Donaldson won a Fields medal for his work in the area. The authors start from the standpoint that the fundamental group and intersection form of a four-manifold provides information about its homology and characteristic classes, but little of its differential topology. It turns out that the classification up to diffeomorphism of four-manifolds is very different from the classification of unimodular forms and that the study of this question leads naturally to the new Donaldson invariants of four-manifolds. A central theme of this book is that the appropriate geometrical tools for investigating these questions come from mathematical physics: the Yang-Mills theory and anti-self dual connections over four-manifolds. One of the many consquences of this theory is that exotic smooth manifolds exist which are homeomorphic but not diffeomorphic to (4, and that large classes of forms cannot be realized as intersection forms whereas distinct manifolds may share the same form. These result have had far-reaching consequences in algebraic geometry, topology, and mathematical physics, and will continue to be a mainspring of mathematical research for years to come. Nº de ref. de la librería AAV9780198502692

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Donaldson, S. K.
Editorial: Clarendon Press (1997)
ISBN 10: 0198502699 ISBN 13: 9780198502692
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Descripción Clarendon Press, 1997. PAP. Estado de conservación: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería LQ-9780198502692

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Kronheimer Donaldson, Research Fellow P B Kronheimer, Professor of Mathematics S K Donaldson
Editorial: Oxford University Press, United Kingdom (1997)
ISBN 10: 0198502699 ISBN 13: 9780198502692
Nuevos Paperback Cantidad: 10
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Descripción Oxford University Press, United Kingdom, 1997. Paperback. Estado de conservación: New. Revised ed.. 244 x 170 mm. Language: English . Brand New Book ***** Print on Demand *****. This book provides the first lucid and accessible account to the modern study of the geometry of four-manifolds. It has become required reading for postgraduates and research workers whose research touches on this topic. Pre-requisites are a firm grounding in differential topology, and geometry as may be gained from the first year of a graduate course. The subject matter of this book is the most significant breakthrough in mathematics of the last fifty years, and Professor Donaldson won a Fields medal for his work in the area. The authors start from the standpoint that the fundamental group and intersection form of a four-manifold provides information about its homology and characteristic classes, but little of its differential topology. It turns out that the classification up to diffeomorphism of four-manifolds is very different from the classification of unimodular forms and that the study of this question leads naturally to the new Donaldson invariants of four-manifolds. A central theme of this book is that the appropriate geometrical tools for investigating these questions come from mathematical physics: the Yang-Mills theory and anti-self dual connections over four-manifolds. One of the many consquences of this theory is that exotic smooth manifolds exist which are homeomorphic but not diffeomorphic to (4, and that large classes of forms cannot be realized as intersection forms whereas distinct manifolds may share the same form. These result have had far-reaching consequences in algebraic geometry, topology, and mathematical physics, and will continue to be a mainspring of mathematical research for years to come. Nº de ref. de la librería AAV9780198502692

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Donaldson, Kronheimer
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Descripción OUP Oxford, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9780198502692_lsuk

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Donaldson, S. K.
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Descripción Clarendon Press, 1997. PAP. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IQ-9780198502692

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Donaldson, S. K.; Kronheimer, P. B.
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Descripción Clarendon Press, 1997. Paperback. Estado de conservación: New. Nº de ref. de la librería INGM9780198502692

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Donaldson, S. K.; Kronheimer, P. B.
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Descripción Oxford University Press, 1997. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0198502699

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S. K. Donaldson, P. B. Kronheimer
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Descripción Oxford University Press, USA, 1997. Paperback. Estado de conservación: New. Nº de ref. de la librería DADAX0198502699

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Donaldson, S. K., Kronheimer, P. B.
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Descripción Clarendon Press, 2017. Paperback. Estado de conservación: New. This item is printed on demand. Nº de ref. de la librería P110198502699

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Descripción Clarendon Press, 2017. Paperback. Estado de conservación: New. This item is printed on demand. Nº de ref. de la librería 0198502699

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