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LEADER: 03196nam a22004695a 4500
001 014157688-X
005 20141003190146.0
008 100301s1993 xxu| o ||0| 0|eng d
020 $a9780817647315
020 $a9780817647308 (ebk.)
020 $a9780817647315
020 $a9780817647308
024 7 $a10.1007/978-0-8176-4731-5$2doi
035 $a(Springer)9780817647315
040 $aSpringer
050 4 $aQA641-670
072 7 $aMAT012030$2bisacsh
072 7 $aPBMP$2bicssc
082 04 $a516.36$223
100 1 $aBrylinski, Jean-Luc,$eauthor.
245 10 $aLoop Spaces, Characteristic Classes and Geometric Quantization /$cby Jean-Luc Brylinski.
264 1 $aBoston, MA :$bBirkhäuser Boston :$bImprint: Birkhäuser,$c1993.
300 $aXVI, 302 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aProgress in Mathematics
505 0 $aComplexes of Sheaves and their Hypercohomology -- Line Bundles and Central Extensions -- Kähler Geometry of the Space of Knots -- Degree 3 Cohomology: The Dixmier-Douady Theory -- Degree 3 Cohomology: Sheaves of Groupoids -- Line Bundles over Loop Spaces -- The Dirac Monopole.
520 $aThis book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Various developments in mathematical physics (e.g., in knot theory, gauge theory, and topological quantum field theory) have led mathematicians and physicists to search for new geometric structures on manifolds and to seek a synthesis of ideas from geometry, topology and category theory. In this spirit, this book develops the differential geometry associated to the topology and obstruction theory of certain fiber bundles (more precisely, associated to grebes). The theory is a 3-dimensional analog of the familiar Kostant--Weil theory of line bundles. In particular the curvature now becomes a 3-form. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, Cheeger--Chern--Simons secondary characteristics classes, and group cohomology. Finally, the last chapter deals with the Dirac monopole and Dirac’s quantization of the electrical charge. The book will be of interest to topologists, geometers, Lie theorists and mathematical physicists, as well as to operator algebraists. It is written for graduate students and researchers, and will be an excellent textbook. It has a self-contained introduction to the theory of sheaves and their cohomology, line bundles and geometric prequantization à la Kostant--Souriau.
650 20 $aTopology.
650 20 $aGeometry, Differential.
650 10 $aMathematics.
650 0 $aAlgebra.
650 0 $aGlobal differential geometry.
650 0 $aMathematics.
650 0 $aTopology.
650 24 $aCategory Theory, Homological Algebra.
776 08 $iPrinted edition:$z9780817647308
830 0 $aProgress in Mathematics.
988 $a20140910
906 $0VEN