Multiplicative K-theory

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  Karoubi: "In this paper we introduce a new type of K-theory, called "multiplicative K-theory" kn(A) for A a Frechet algebra, which is intermediary between algebraic K-theory, denoted Kn(A), and topological K-theory, denoted Kntop(A). This new theory is computable in terms of Kntop(A) and cyclic homology HC*(A). The homomorphism from Kn(A) to kn(A) we define in the paper detects all known primary and secondary characterictic classes from algebraic K-theory to cyclic homology (for example the Borel regulator if A = the field of complex numbers). It is related to the multiplicative character of a Fredholm module defined previously by A. Connes and the author."

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• Paper References

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• Definition

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• Properties

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• Standard theorems

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• Open Problems

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• Connections to Number Theory

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• Computations and Examples

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• History and Applications

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• Some Research Articles

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• Other Information

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• General Introduction
• Search results
• Online References
• Paper References
• Definition
• Properties
• Standard theorems
• Open Problems
• Connections to Number Theory
• Computations and Examples
• History and Applications
• Some Research Articles
• Other Information
• Comments Posted
• Comments