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Semi-topological K-Theory

In: Handbook of K-Theory

Author

Listed:
  • Eric M. Friedlander

    (Northwestern University, Department of Mathematics)

  • Mark E. Walker

    (University of Nebraska – Lincoln, Department of Mathematics)

Abstract

The semi-topological K-theory of a complex variety X, written K * sst (X), interpolates between the algebraic K-theory, K * alg (X), of X and the topological K-theory, K top * (X an ), of the analytic space (X an ) associated to X. (The superscript “sst” stands for “singular semi-topological”.) In a similar vein, the real semi-topological K-theory, written Kℝ * sst (Y), of a real variety Y interpolates between the algebraic K-theory of Y and the Atiyah Real K-theory of the associated space with involution Y ℝ(ℂ). We intend this survey to provide both motivation and coherence to the field of semi-topological K-theory. We explain the many foundational results contained in the series of papers by the authors [27, 31, 32], as well as in the recent paper by the authors and Christian Haesemeyer [21]. We shall alsomention various conjectures that involve challenging problems concerning both algebraic cycles and algebraic K-theory.

Suggested Citation

  • Eric M. Friedlander & Mark E. Walker, 2005. "Semi-topological K-Theory," Springer Books, in: Eric M. Friedlander & Daniel R. Grayson (ed.), Handbook of K-Theory, chapter 0, pages 877-924, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27855-9_17
    DOI: 10.1007/978-3-540-27855-9_17
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