Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor "Schick, Thomas Prof. Dr."
Now showing items 120 of 29

The Spectra on Lie Groups and Its Application to twisted L2Invariants
(20240229)We computed spectra of various $G$invariant differential operators on the universal cover of 2x2 unimodular groups. This was achieved by applying tools from harmonic analysis/representation theory to corresponding groups. ... 
Twisted equivariant Ktheory and equivariant Tduality
(20230918)This thesis is about two things: twisted equivariant Ktheory and equivariant topological Tduality. First, we prove a fixed point decomposition theorem for twisted equivariant Ktheory, generalising a result of Atiyah and ... 
NovikovShubin Invariants of Nilpotent Lie Groups
(20230525)NovikovShubin invariants are socalled L2invariants of noncompact manifolds. They are defined using the Laplace operators and measure the density of their spectra near zero. This nearzero part of the spectrum is ... 
Concordances in Positive Scalar Curvature and Index Theory
(20230224)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
(20211111)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 ... 
L²Invariants for SelfSimilar CWComplexes
(20201111)L²invariants are commonly defined only for periodic spaces, that is, spaces with a cocompact action by some discrete group. This thesis develops a theory of L²invariants for quasiperiodic spaces instead, where the group ... 
Index Theory and Positive Scalar Curvature
(20200724)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 ... 
BenjaminiSchramm Convergence of Normalized Characteristic Numbers of Riemannian Manifolds
(20200430)We study a weak form of GromovHausdorff convergence of Riemannian manifolds, also known as BenjaminiSchramm convergence. This concept is also applicable to other areas and has widely been studied in the context of ... 
A MayerVietoris Spectral Sequence for C*Algebras and Coarse Geometry
(20190410)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 ... 
Shape space in terms of Wasserstein geometry and application to quantum physics
(20181126)This thesis offers a mathematical framework to treat quantum dynamics without reference to a background structure, but rather by means of the change of the shape of the state. For this, Wasserstein geometry is used. The ... 
New topological and index theoretical methods to study the geometry of manifolds
(20180731)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 ... 
Characters on infinite groups and rigidity
(20180502)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 ... 
Secondary largescale index theory and positive scalar curvature
(20160906)We develop a theory of secondary invariants associated to complete Riemannian metrics of uniformly positive scalar curvature outside a prescribed subset on a spin manifold. We work in the context of largescale (or "coarse") ... 
On an analogue of L2Betti numbers for finite field coefficients and a question of Atiyah
(20160712)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 L2Betti numbers and thus allows an analogue definition for finite ... 
Geometric twisted Khomology, Tduality isomorphism and Tduality for circle actions
(20151116)We discuss topological Tduality 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 Khomology are ... 
Algebraic Structure and Integration in Generalized Differential Cohomology
(20140122)The present thesis deals with the construction of algebraic structure, particularly products, on generalized differential cohomology from an abstract homotopytheoretic point of view. Beginning with a multiplicative ... 
Categorification and applications in topology and representation theory
(20130828)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 BarNatan's ... 
L2invariants of nonuniform lattices in semisimple Lie groups
(20130503)We compute L²invariants of certain nonuniform lattices in semisimple Lie groups by means of the BorelSerre compactification of arithmetically defined locally symmetric spaces. The main results give new estimates for ... 
Index Theory and Positive Scalar Curvature
(20120622)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 DiracRosenberg ... 
Higher Lefschetz invariants for foliated manifolds
(20120522)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 ...