D-Branes, Tachyons and K-Homology

Abstract

We present an overview of the ways in which D-brane charges are classified in terms of K-theory, emphasizing the natural physical interpretations of a homological classification within a topological setting.

18 pages AMSTeX, 3 eps figures; Based on invited lecture given at the Workshop on Algebraic Geometry and Physics ``K-Theory, Derived Categories and Strings'', University of Genoa, Genoa, Italy, June 18-21 2002; V2: Clarifying comments and reference added

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• Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory
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• Quantum D-branes and exotic smooth R^4
• Topics on D-brane charges with B-fields
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• Commutative Geometry for Non-commutative D-branes by Tachyon Condensation
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• Exceptional Periodicity and Magic Star Algebras. I : Foundations
• KO-Homology and Type I String Theory
• D-branes, KK-theory and duality on noncommutative spaces
• Exotic smooth R^4, geometry of string backgrounds and quantum D-branes
• D-Branes in Noncommutative Field Theory
• K-theory in cutoff version of Vacuum String Field Theory
• The Construction of Dirac Operators on Orientifolds