2005 | OriginalPaper | Buchkapitel
Semi-topological K-Theory
verfasst von : Eric M. Friedlander, Mark E. Walker
Erschienen in: Handbook of K-Theory
Verlag: Springer Berlin Heidelberg
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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 *(Xan), of the analytic space (Xan) 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 Yℝ(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.