Semi-topological K-Theory

Eric M. Friedlander () and Mark E. Walker ()
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Eric M. Friedlander: Northwestern University, Department of Mathematics
Mark E. Walker: University of Nebraska – Lincoln, Department of Mathematics

Chapter V.1 in Handbook of K-Theory, 2005, pp 877-924 from Springer

Abstract: 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.

Keywords: Spectral Sequence; Chern Character; Algebraic Cycle; Topological Abelian Group; Projective Complex Variety (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/978-3-540-27855-9_17

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