Land, Markus ; Nikolaus, Thomas
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
|---|
| Titel eines Journals oder einer Zeitschrift: | Mathematische Annalen |
|---|
| Verlag: | SPRINGER HEIDELBERG |
|---|
| Ort der Veröffentlichung: | HEIDELBERG |
|---|
| Band: | 371 |
|---|
| Nummer des Zeitschriftenheftes oder des Kapitels: | 1-2 |
|---|
| Seitenbereich: | S. 517-563 |
|---|
| Datum: | 2018 |
|---|
| Institutionen: | Mathematik |
|---|
| Identifikationsnummer: | | Wert | Typ |
|---|
| 10.1007/s00208-017-1617-0 | DOI |
|
|---|
| Stichwörter / Keywords: | CATEGORIES; HOMOLOGY; LOCALIZATION; SPECTRA; |
|---|
| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
|---|
| Status: | Veröffentlicht |
|---|
| Begutachtet: | Ja, diese Version wurde begutachtet |
|---|
| An der Universität Regensburg entstanden: | Ja |
|---|
| Dokumenten-ID: | 47173 |
|---|
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.
Altmetric