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 Vector Bundles in Algebraic Geometry Successive waves of migrant concepts, largely from mathematical physics, have stimulated the study of vector bundles over algebraic varieties in the past few years. But the subject has retained its roots in old questions concerning subvarieties of projective space. The 1993 Durham Symposium on vector bundles in algebraic geometry brought together some of the leading researchers in the field to further explore these interactions. This book is a collection of survey articles by the main speakers at the Symposium and presents to the mathematical world an overview of the key areas of research involving vector bundles. Topics include augmented bundles and coherent systems which link gauge theory and geometric invariant theory; Donaldson invariants of algebraic surfaces; Floer homology and quantum cohomology; conformal field theory and the moduli spaces of bundles on curves; the Horrocks-Mumford bundle and codimension 2 subvarieties in p4 and p5; and exceptional bundles and stable sheaves on projective space. This book will appeal greatly to mathematicians working in algebraic geometry and areas adjoining mathematical physics.
 Topology of Fibre Bundles by Norman Steenrod, Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.
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