Bunke, Ulrich ; Nikolaus, Thomas ; Völkl, Michael
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Journal of Homotopy and Related Structures |
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| Verlag: | SPRINGER HEIDELBERG |
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| Ort der Veröffentlichung: | HEIDELBERG |
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| Band: | 11 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 1 |
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| Seitenbereich: | S. 1-66 |
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| Datum: | 2016 |
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| Institutionen: | Mathematik > Prof. Dr. Ulrich Bunke |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1007/s40062-014-0092-5 | DOI |
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| Stichwörter / Keywords: | ; Differential cohomology; Sheaves on manifolds; Stable infinity categories |
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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: | 41879 |
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Zusammenfassung
We show that every sheaf on the site of smooth manifolds with values in a stable (infinity, 1)-category (like spectra or chain complexes) gives rise to a "differential cohomology diagram" and a homotopy formula, which are common features of all classical examples of differential cohomology theories. These structures are naturally derived from a canonical decomposition of a sheaf into a homotopy ...
Zusammenfassung
We show that every sheaf on the site of smooth manifolds with values in a stable (infinity, 1)-category (like spectra or chain complexes) gives rise to a "differential cohomology diagram" and a homotopy formula, which are common features of all classical examples of differential cohomology theories. These structures are naturally derived from a canonical decomposition of a sheaf into a homotopy invariant part and a piece which has a trivial evaluation on a point. In the classical examples the latter is the contribution of differential forms. This decomposition suggests a natural scheme to analyse new sheaves by determining these pieces and the gluing data. We perform this analysis for a variety of classical and not so classical examples.
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