Land, Markus ; Nikolaus, Thomas
Alternative Links zum Volltext:DOIVerlag
Dokumentenart: | Artikel |
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Titel eines Journals oder einer Zeitschrift: | Mathematische Annalen |
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Verlag: | SPRINGER HEIDELBERG |
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Ort der Veröffentlichung: | HEIDELBERG |
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Band: | 371 |
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Nummer des Zeitschriftenheftes oder des Kapitels: | 1-2 |
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Seitenbereich: | S. 517-563 |
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Datum: | 2018 |
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Institutionen: | Mathematik |
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Identifikationsnummer: | Wert | Typ |
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10.1007/s00208-017-1617-0 | DOI |
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Stichwörter / Keywords: | CATEGORIES; HOMOLOGY; LOCALIZATION; SPECTRA; |
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Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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Status: | Veröffentlicht |
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Begutachtet: | Ja, diese Version wurde begutachtet |
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An der Universität Regensburg entstanden: | Ja |
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Dokumenten-ID: | 47173 |
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Zusammenfassung
We prove the existence of a map of spectra between connective topological K-theory and connective algebraic L-theory of a complex -algebra A which is natural in A and compatible with multiplicative structures. We determine its effect on homotopy groups and as a consequence obtain a natural equivalence of periodic K- and L-theory spectra after inverting 2. We show that this equivalence extends to ...
Zusammenfassung
We prove the existence of a map of spectra between connective topological K-theory and connective algebraic L-theory of a complex -algebra A which is natural in A and compatible with multiplicative structures. We determine its effect on homotopy groups and as a consequence obtain a natural equivalence of periodic K- and L-theory spectra after inverting 2. We show that this equivalence extends to K- and L-theory of real -algebras. Using this we give a comparison between the real Baum-Connes conjecture and the L-theoretic Farrell-Jones conjecture. We conclude that these conjectures are equivalent after inverting 2 if and only if a certain completion conjecture in L-theory is true.