Parametrised simplicial volume and S¹-actions

URN to cite this document:: urn:nbn:de:bvb:355-epub-404319
DOI to cite this document:: 10.5283/epub.40431

Fauser, Daniel

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Date of publication of this fulltext: 03 Jul 2019 07:46

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Item type:	Thesis of the University of Regensburg (PhD)
Open Access Type:	Primary Publication
Date:	3 July 2019
Referee:	Prof. Dr. Clara Löh
Date of exam:	27 June 2019
Institutions:	Mathematics > Prof. Dr. Clara Löh
Keywords:	simplicial volume, integral foliated simplicial volume, aspherical manifolds, S^1-actions
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:	40431

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Abstract (English)

In this work, we study integral approximations of the simplicial volume. The simplicial volume is a homotopy invariant of oriented closed connected manifolds introduced by Gromov in the late 70's. Following the approach of Yano in the classical case, we prove that the integral foliated simplicial volume of aspherical oriented closed connected smooth manifolds with non-trivial smooth S^1-action vanishes.

Translation of the abstract (German)

In dieser Arbeit studieren wir ganzzahlige Approximationen des Simplizialen Volumens. Das simpliziale Volumen ist eine Homotopieinvariante für orientierte geschlossene zusammenhängende Mannigfaltigkeiten, welche von Gromov in den späten 70ern eingeführt wurde. Wir folgen Yanos Ausführungen im klassischen Fall, um zu zeigen, dass das ganzzahlige geblätterte simpliziale Volumen von asphärischen ...