Differential Forms on Tropical Spaces

URN to cite this document:: urn:nbn:de:bvb:355-epub-362621
DOI to cite this document:: 10.5283/epub.36262

Smacka, Jascha

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Date of publication of this fulltext: 27 Oct 2017 09:49

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Item type:	Thesis of the University of Regensburg (PhD)
Date:	27 October 2017
Referee:	Prof. Dr. Walter Gubler
Date of exam:	27 July 2017
Institutions:	Mathematics > Prof. Dr. Walter Gubler
Keywords:	Tropical manifolds, differential forms, currents, homological algebra, derived categories, ddc-lemma, Bott-Chern cohomology, Aeppli cohomology
Dewey Decimal Classification:	500 Science > 510 Mathematics
Status:	Published
Refereed:	Yes, this version has been refereed
Created at the University of Regensburg:	Yes
Item ID:	36262

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Abstract (English)

We show some basic cohomological properties of the double complex of differential forms on tropical spaces and the associated derived dual complexes. We then use these results to show that the tropical projective space satisfies an analogue of the ddc -lemma for complex manifolds.

Translation of the abstract (German)

Wir zeigen einige einfache kohomologische Eigenschaften des Doppelkomplexes von Differentialformen sowie assoziierter dualer Komplexe auf tropischen Räumen. Diese nutzen wir, um zu zeigen dass der tropische projektive Raum ein Analogon des klassischen ddc-Lemmas auf komplexen Mannigfaltigkeiten erfüllt.

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