Ara, Dimitri ; Métayer, François
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| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Homology, Homotopy and Applications |
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| Verlag: | INT PRESS BOSTON, INC |
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| Ort der Veröffentlichung: | SOMERVILLE |
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| Band: | 13 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 1 |
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| Seitenbereich: | S. 121-142 |
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| Datum: | 2011 |
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| Institutionen: | Mathematik |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.4310/HHA.2011.v13.n1.a6 | DOI |
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| Stichwörter / Keywords: | PARALLEL TRANSPORT; GERBES; HOLONOMY; connection; gerbe; 2-group; path 2-groupoid; parallel transport |
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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: | 65397 |
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Zusammenfassung
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory and differential geometry. We show that smooth 2-functors appear in several fields, namely as connections on (non-abelian) gerbes, as derivatives of ...
Zusammenfassung
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory and differential geometry. We show that smooth 2-functors appear in several fields, namely as connections on (non-abelian) gerbes, as derivatives of smooth functors and as critical points in BF theory. We demonstrate further that our dictionary provides a powerful tool to discuss the transgression of geometric objects to loop spaces.
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