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Sutured manifolds, L²-Betti numbers and an upper bound on the leading coefficient

Herrmann, Gerrit (2019) Sutured manifolds, L²-Betti numbers and an upper bound on the leading coefficient. PhD, Universität Regensburg.

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Date of publication of this fulltext: 26 Jul 2019 08:15

Abstract (English)

In this thesis the author shows that a sutured manifold is taut if and only if certain relativ L^2-Betti numbers are zero. As a consequence one obtains a relativ L^2-torsion for taut sutured manifolds. The author studies this L^2-torsion and relates it the the leading coefficient defined by Liu.

Translation of the abstract (German)

In dieser Arbeit zeigt der Autor, dass eine genähte Mannigfaltigkeit straff ist genau dann, wenn bestimmte relative L^2-Betti Zahlen verschwinden. Als Konsequenz existiert die relative L^2-Torsion für straff genähte Mannigfaltigkeiten. Der Autor untersucht diese L^2-Torsion und vergleicht sie mit Liu's Leitkoeffizient.

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Item type:Thesis of the University of Regensburg (PhD)
Date:26 July 2019
Referee:Prof. Dr. Stefan Friedl
Date of exam:11 July 2019
Institutions:Mathematics > Prof. Dr. Stefan Friedl
Keywords:L^2-Betti numbers, sutured manifolds, taut, L^2-Alexander torsion, L^2-torsion, 3-manifold, Thurston norm,
Dewey Decimal Classification:500 Science > 510 Mathematics
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:40578
Owner only: item control page


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