Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Gutachter "Schick, Thomas 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 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 ... -
A Wasserstein-like Distance on Vector Fields
(2023-10-06)We introduce a new distance on the space of vector fields over a Riemannian manifold that is motivated by the construction and properties of the Wasserstein distance. The construction relies on a particular metric on 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 ... -
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 ... -
Analytic singularities near radial points
(2015-03-11)In this thesis, we applied tools of algebraic analysis and knowledge of symplectic geometry and contact geometry to give a normal form of certain class of microdifferential operators, and then studied analytic singularities of ... -
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 ... -
Azumaya-Algebren und Oktavenalgebren auf algebraischen Varietäten
(2013-11-21)We study noncommutative algebras over rings and on algebraic varieties. In the first part we give a criterion for whether or how far a central simple algebra over the function field of a projective variety could be extended ... -
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 ... -
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 ... -
Computation with finitely L-presented groups
(2012-06-20)We develop algorithms for certain infinitely presented groups, the so-called finitely L-presented groups. For this purpose, we generalize the well-known algorithms for finitely presented groups to finite L-presentations. ... -
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 ... -
Conformal Properties of Generalized Dirac Operator
(2013-07-24)In this thesis we study the non-linear Dirac operator in dimension four and the associated generalization of the Seiberg-Witten equations in dimension four. The central object of this generalization is a hyperK ahler ... -
Continuous Wavelet Transformation on Homogeneous Spaces
(2021-03-29)The classical Continuous Wavelet Transformation (cCWT) is an important and well-studied tool in signal processing and data analysis. Because of its deep connection to representation theory, it has come into focus of pure ... -
Critical exponents for semilinear Tricomi-type equations
(2016-11-24)In this thesis, we consider the semilinear Tricomi-type equations. In particular, we work on the global Cauchy problem for the semilinear Tricomi-type equation with suitable initial data. The main objective of this thesis ... -
Discrete and Profinite Groups Acting on Regular Rooted Trees
(2010-01-14)We develop a new method to investigate groups acting on rooted trees. Considering the set of continuous functions from the automorphism group $\operatorname{Aut}X^*$ of a regular rooted tree to a finite field, we associate ... -
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 ... -
Generalizations of Quandles to Multi-Linkoids
(2024-04-10)In this thesis, we define the fundamental quandle of knotoids and linkoids and prove that it is invariant under the under forbidden-move and hence encodes only the information of the underclosure of the knotoid. We ...