Cover image for Noncommutative geometry and physics. 3. Shonan Village Center, Japan, 18-22 February 2008 ; Kyoto University, Japan, 1 April 2010-31 March 2011 / edited by Guiseppe Dito ... [et al.].
Title:
Noncommutative geometry and physics. 3. Shonan Village Center, Japan, 18-22 February 2008 ; Kyoto University, Japan, 1 April 2010-31 March 2011 / edited by Guiseppe Dito ... [et al.].
Series:
Noncommutative geometry and physics ; v. 3
Publication Information:
Singapore ; London : World Scientific, c2013.
Physical Description:
viii, 528 p. ; 26 cm.
ISBN:
9789814425001
General Note:
Selected conference papers from a workshop held in Feb. 2008 in Kyoto Japan on "K-theory and D-branes",
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30000010312235 QC20.7.D52 N665 2013 Open Access Book Book
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Summary

Summary

Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics.


Table of Contents

Alan L. Carey and John Phillips and Adam Rennie and Fedor A. SukochevAlan L. Carey and John Phillips and Adam RennieTetsuji KimuraAkifumi SakoRichard J. SzaboDai TamakiDai TamakiKazufumi Kimoto and Masato WakayamaQin WangPaolo Bertozzini and Roberto Conti and Wicharn LewkeeratiyutkulJonathan Block and Nigel HigsonPeter Bouwknegt and Alan Carey and Rishni RatnamKatsutoshi KawashimaFrancesco D'Andrea and Giovanni LandiHyun Ho LeeShin-ichi OguniYoshiaki Maeda and Akifumi SakoJonathan RosenbergPaulo Carrillo Rouse
Prefacep. v
Part I K-Theory and D-Branes, Shonan
The Local Index Formula in Noncommutative Geometry Revisitedp. 3
Semi-Finite Noncommutative Geometry and Some Applicationsp. 37
Generalized Geometries in String Compactification Scenariosp. 59
What Happen to Gauge Theories under Noncommutative Deformation?p. 111
D-Branes and Bivariant K-Theoryp. 131
Two-Sided Bar Constructions for Partial Monoids and Applications to K-Homology Theoryp. 177
Twisting Segal's K-Homology Theoryp. 197
Spectrum of Non-Commutative Harmonic Oscillators and Residual Modular Formsp. 237
Coarse Embeddings and Higher Index Problems for Expandersp. 269
Part II Deformation Quantization and Noncommutative Geometry, RIMS
Enriched Fell Bundles and Spaceoidsp. 283
Weyl Character Formula in KK-Theoryp. 299
Recent Advances in the Study of the Equivariant Brauer Groupp. 335
Entire Cyclic Cohomology of Noncommutative Manifoldsp. 359
Geometry of Quantum Projective Spacesp. 373
On Yang-Mills Theory for Quantum Heisenberg Manifoldsp. 417
Dilatational Equivalence Classes and Novikov-Shubin Type Capacities of Groups, and Random Walksp. 433
Deformation Quantization of Gauge Theory in R 4 and U(1) Instanton Problemsp. 471
Dualities in Field Theories and the Role of K-Theoryp. 485
Deformation Groupoids and Pushforward Maps in Twisted K-Theoryp. 507