Semitopological Khomology

General Introduction
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Search results
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Online References
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Paper References
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Definition
Walker: Semitopological Khomology and Thomason's Theorem, by Mark E. Walker. In this paper, we introduce the "semitopological Khomology" of complex varieties, a theory related to semitopological Ktheory much as connective topological Khomology is related to connective topological Ktheory. Our main theorem is that the semitopological Khomology of a smooth, quasiprojective complex variety Y coincides with the connective topological Khomology of the analytic space associated to Y. From this result, we deduce a pair of results relating semitopological Ktheory with connective topological Ktheory. In particular, we prove that the "Bott inverted" semitopological Ktheory of a smooth, projective complex variety X coincides with the topological Ktheory of its analytic realization. In combination with a result of Friedlander and the author, this gives a new proof, in the special case of smooth, projective complex varieties, of Thomason's celebrated theorem that "Bott inverted" algebraic Ktheory with finite coefficients coincides with topological Ktheory with finite coefficients.
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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
arXiv:1206.0690 Equivariant semitopological Khomology and a theorem of Thomason from arXiv Front: math.KT by Jeremiah Heller, Jens Hornbostel We generalize several comparison results between algebraic, semitopological and topological Ktheories to the equivariant case with respect to a finite group. Moreover, we show that Walker's theorem comparing semitopological and topological Khomology extends to singular varieties.
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Other Information
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