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The Comparison of K-Theory and TC

  • Chapter
The Local Structure of Algebraic K-Theory

Part of the book series: Algebra and Applications ((AA,volume 18))

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Abstract

This chapter begins with a proof that the difference between algebraic K-theory and topological cyclic homology is “locally constant” by means of a hands-on approach, nesting our way down from the fact that stable K-theory is topological Hochschild homology.

The chapter finishes with an overview of the state of affairs with respect to the calculations of algebraic K-theory obtained via trace methods.

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Authors and Affiliations

  1. Department of Mathematics, University of Bergen, Bergen, Norway

    Bjørn Ian Dundas

  2. Mathematics Department, Brown University, Providence, USA

    Thomas G. Goodwillie

  3. Department of Mathematics, University of Illinois, Urbana, IL, USA

    Randy McCarthy

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  1. Bjørn Ian Dundas
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  2. Thomas G. Goodwillie
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  3. Randy McCarthy
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Dundas, B.I., Goodwillie, T.G., McCarthy, R. (2013). The Comparison of K-Theory and TC . In: The Local Structure of Algebraic K-Theory. Algebra and Applications, vol 18. Springer, London. https://doi.org/10.1007/978-1-4471-4393-2_7

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