Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Gutachter "Meyer, Ralf Prof. Dr."
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A classification of localizing subcategories by relative homological algebra
(2015-12-17)In this thesis, we use the tools of relative homological algebra in triangulated categories to define a sensible notion of support for objects in the bootstrap class of a Kasparov category of C*-algebras over a finite ... -
A colimit construction for groupoids
(2016-08-03)We consider Ore monoid actions in a certain bicategory of étale groupoids Gr_prop. Examples of such actions include self-similar groups, higher rank graphs and actions of Ore monoids on spaces by topological correspondences. ... -
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 ... -
Algorithms for structured nonconvex optimization: theory and practice
(2018-07-24)We first synthesize and unify notions of regularity, both of individual functions/sets and of families of functions/sets, as they appear in the convergence theory of fixed point iterations. Several new primal and dual ... -
An Integration Theorem for Representations of the Tangent Algebroid
(2024-02-09)This dissertation investigates representations of Lie groupoids and Lie algebroids and the connection between them. Lie groupoids and Lie algebroids are differential-geometric generalisations of Lie groups and Lie ... -
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 ... -
C*-quantum groups with projection
(2014-06-25)We propose a general theory to study semidirect products of C -quantum groups in the framework of multiplicative unitaries. Starting from a quantum group with a projection we decompose its multiplicative unitary as a product ... -
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 ... -
Coarse Geometry for Noncommutative Spaces
(2016-11-23)We develop an analogoue of coarse geometry for noncommutative spaces in terms of unitizations of the given C* -algebra. Examples for our theory come from Rieffel deformation of compactifications under strongly continuous ... -
Exakte Moduln über dem von Manuel Köhler beschriebenen Ring
(2018-11-13)When proving an equivariant universal coefficient theorem for C*-Algebras acted on by a finite cyclic group Z/pZ, Manuel Köhler introduces the endomorphism ring R of the tuple (C,C(G),D). The aim of this thesis is to show ... -
Explicit GL(2) trac formulas and uniform, mixed Weyl laws
(2012-10-24)This thesis provides an explicit, general trace formula for the Hecke and Casimir eigenvalues of GL(2)-automorphic representations over a global field. In special cases, we obtain Selberg's original trace formula. Computations ... -
Groupoids in categories with partial covers
(2019-02-07)Meyer and Zhu survey the general theory of groupoids, groupoid actions, groupoid principal bundles, and various kinds of morphisms between groupoids in the framework of categories with pretopology. We modify the categorical ... -
Higher Groupoid Actions, Bibundles, and Differentiation
(2014-08-13)In this thesis, we employ simplicial methods to study actions, principal bundles and bibundles of higher groupoids. Roughly, we use Kan fibrations to model actions of higher groupoids; we use pairs of a Kan fibration ... -
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 ... -
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 ... -
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 ... -
Noncommutative manifolds and Seiberg-Witten-equations
(2011-10-17)In this thesis we study differential geometry of noncommutative manifolds. We introduce a general framework of noncommutative manifolds based on Poincaré duality and study the notions of differential forms and Sobolev ... -
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 ...