Noncommutative Geometry And Physics 3: Proceedings Of The Noncommutative Geometry And Physics 2008, On K-Theory And D-Branes & Proceedings Of The Rims Thematic Year 2010 On Perspectives In Deformation Quantization And Noncommutative Geometry, 1st Edition

  • Published By: World Scientific Publishing Company
  • ISBN-10: 981442501X
  • ISBN-13: 9789814425018
  • DDC: 530.15635
  • Grade Level Range: College Freshman - College Senior
  • 536 Pages | eBook
  • Original Copyright 2013 | Published/Released January 2015
  • This publication's content originally published in print form: 2013

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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

Front Cover.
Half Title Page.
Other Frontmatter.
Title Page.
Copyright Page.
1: K-Theory and D-Branes, Shonan.
2: The Local Index Formula in Noncommutative Geometry Revisited.
3: Semi-Finite Noncommutative Geometry and Some Applications.
4: Generalized Geometries in String Compactification Scenarios.
5: What Happen to Gauge Theories under Noncommutative Deformation?.
6: D-Branes and Bivariant K-Theory.
7: Two-Sided Bar Constructions for Partial Monoids and Applications to K-Homology Theory.
8: Twisting Segal's K-Homology Theory.
9: Spectrum of Non-Commutative Harmonic Oscillators and Residual Modular Forms.
10: Coarse Embeddings and Higher Index Problems for Expanders.
11: Deformation Quantization and Noncommutative Geometry, RIMS.
12: Enriched Fell Bundles and Spaceoids.
13: Weyl Character Formula in KK-Theory.
14: Recent Advances in the Study of the Equivariant Brauer Group.
15: Entire Cyclic Cohomology of Noncommutative Manifolds.
16: Geometry of Quantum Projective Spaces.
17: On Yang-Mills Theory for Quantum Heisenberg Manifolds.
18: Dilatational Equivalence Classes and Novikov-Shubin Type Capacities of Groups, and Random Walks.
19: Deformation Quantization of Gauge Theory in ℝ4 and U(1) Instanton Problems.
20: Dualities in Field Theories and the Role of K-Theory.
21: Deformation Groupoids and Pushforward Maps in Twisted K-Theory.