Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor "Schick, Thomas Prof. Dr."
Now showing items 1-20 of 27
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A Mayer-Vietoris Spectral Sequence for C*-Algebras and Coarse Geometry
(2019-04-10)Let $A$ be a C*-algebra that is the norm closure $A = \overline{\sum_{\beta \in \alpha} I_\beta}$ of an arbitrary sum of C*-ideals $I_\beta \subseteq A$. We construct a homological spectral sequence that takes as input the ... -
Algebraic Structure and Integration in Generalized Differential Cohomology
(2014-01-22)The present thesis deals with the construction of algebraic structure, particularly products, on generalized differential cohomology from an abstract homotopy-theoretic point of view. Beginning with a multiplicative ... -
Approximation of center-valued Betti-numbers and the center-valued Atiyah-conjecture
(2009-11-25)In the Thesis, we extend Lück"s approximation theorem for Betti-numbers to center-valued Betti-numbers. This allows to classify homology modules of G-CW complexes by looking at there finite dimensional analogues. In ... -
Benjamini-Schramm Convergence of Normalized Characteristic Numbers of Riemannian Manifolds
(2020-04-30)We study a weak form of Gromov-Hausdorff convergence of Riemannian manifolds, also known as Benjamini-Schramm convergence. This concept is also applicable to other areas and has widely been studied in the context of ... -
Categorification and applications in topology and representation theory
(2013-08-28)This thesis splits into two major parts. The connection between the two parts is the notion of "categorification" which we shortly explain/recall in the introduction. In the first part of this thesis we extend Bar-Natan's ... -
Characteristic classes of vector bundles with extra structure
(2007-02-05)This work is about properties of characteristic cohomology classes which occur when a special structure on vector bundles is given. I have focused on two different types of these structures, treated in two independent parts. ... -
Characters on infinite groups and rigidity
(2018-05-02)We show that for a strong extension of discrete measured groupoids $1\to\mathcal{S}\to\mathcal{G}\to\mathcal{Q}\to 1$ with $L\mathcal{G}$ a finite factor, $\mathcal{Q}$ has poperty (T) if and only if the inclusion of ... -
Concordances in Positive Scalar Curvature and Index Theory
(2023-02-24)We apply the strategy to study of diffeomorphisms via block diffeomorphisms to the world of positive scalar curvature (psc) metrics. For each closed psc manifold, we construct the cubical set of all psc block metrics, the ... -
Foliated Positive Scalar Curvature
(2021-11-11)In this thesis we study different questions on scalar curvatures. The first part is devoted to obstructions against existence of a (Riemannian) metric with positive scalar curvature on a closed manifold. The second ... -
Geometric twisted K-homology, T-duality isomorphism and T-duality for circle actions
(2015-11-16)We discuss topological T-duality and the associated geometric or topological objects in this thesis. Concretely, it consists of three parts. In this first part we prove two versions of geometric twisted K-homology are ... -
Higher Lefschetz invariants for foliated manifolds
(2012-05-22)Let $(M, F)$ be a compact foliated manifold. Suppose that a compact Lie group $Γ$ acts on $(M, F)$ by diffeomorphisms of Mthat map each leaf onto itself. We call such a structure a foliated $Γ$ -manifold and denote it ... -
Index Theory and Positive Scalar Curvature
(2020-07-24)The aim of this dissertation is to use relative higher index theory to study questions of existence and classification of positive scalar curvature metrics on manifolds with boundary. First we prove a theorem relating ... -
Index Theory and Positive Scalar Curvature
(2012-06-22)Obstructions to the existence of positive scalar curvature metrics are considered. This thesis has two fairly independent parts. The first part of this thesis proves that the Roe (or coarse) index of the Dirac-Rosenberg ... -
L2-invariants of nonuniform lattices in semisimple Lie groups
(2013-05-03)We compute L²-invariants of certain nonuniform lattices in semisimple Lie groups by means of the Borel-Serre compactification of arithmetically defined locally symmetric spaces. The main results give new estimates for ... -
l<sup>p</sup>-Kohomologie, insbesondere Verschwindungssätze für l<sup>p</sup>-Kohomologie
(2007-08-14)In this dissertation we study the lp-cohomology of discrete groups of type FPn. We give a duality statement and prove some vanishing results, in particular for groups with an ... -
L²-Invariants for Self-Similar CW-Complexes
(2020-11-11)L²-invariants are commonly defined only for periodic spaces, that is, spaces with a cocompact action by some discrete group. This thesis develops a theory of L²-invariants for quasi-periodic spaces instead, where the group ... -
New topological and index theoretical methods to study the geometry of manifolds
(2018-07-31)For a $\mathit{Spin}$ manifold $M$ the Rosenberg index $\alpha([M])$ is an obstruction against positive scalar curvature metrics. When $M$ is non-$\mathit{Spin}$ but $\mathit{Spin}^c$, Bolotov and Dranishnikov suggested ... -
Novikov-Shubin Invariants of Nilpotent Lie Groups
(2023-05-25)Novikov-Shubin invariants are so-called L2-invariants of non-compact manifolds. They are defined using the Laplace operators and measure the density of their spectra near zero. This near-zero part of the spectrum is ... -
On an analogue of L2-Betti numbers for finite field coefficients and a question of Atiyah
(2016-07-12)We construct a dimension function for modules over the group ring of an amenable group. This may replace the von Neumann dimension in the definition of L2-Betti numbers and thus allows an analogue definition for finite ... -
Reduktionssysteme zur Berechnung einer Auflösung der orthogonalen freien Quantengruppen A<sub>o</sub>(n)
(2008-07-29)For the free orthogonal quantum groups Ao(n) we give and verify a complete reduction system. In case of n = 2 we give a finite automat to find every basis element.Futhermore we give a basis ...