Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Gutachter "Schick, Thomas Prof. Dr."
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Generalized Seiberg-Witten and the Nahm Transform
(2019-01-11)Using the viewpoint of principal bundles on hyperk¨ ahler reductions, we recover the results of Gocho and Nakajima [GN92] and give insights into the role that the quater- nions play. We define a framework for dimensional ... -
Generalized Seiberg-Witten equations and hyperKähler geometry
(2006-09-18)In this thesis we study a certain generalization of the gauge-theoretical Seiberg-Witten equations over a source 4-manifold X. The generalization involves a hyperKähler manifold M with ... -
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 groupoids for filtered manifolds
(2020-12-21)In this thesis, we propose to use generalized fixed point algebras as an approach to the pseudodifferential calculus on filtered manifolds. A filtered manifold is a manifold \(M\) with a filtration of its tangent ... -
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 ... -
Investigations in Hadamard spaces
(2021-08-27)This thesis investigates the interplay between geometry and convex analysis in Hadamard spaces. Motivated by numerous applications of CAT(0) geometry, our work builds upon the results in convex analysis and Alexandrov ... -
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 ... -
Lie Algebras and the Dimension Problem
(2021-11-03)The dimension subgroup problem and the Ore conjecture are two group theoretical problems. In this thesis, translations of these problems to Lie algebras are analyzed and partially solved. -
Die lokale Struktur von T-Dualitätstripeln
(2007-12-06)There are different approaches for a mathematical understanding of T-duality. We show that the C*-algebraic approach of Mathai and Rosenberg is equivalent to the topological approach of ... -
Nahms Equations and Nilpotent Orbits
(2022-05-31)P. Kronheimer has identified certain space of solutions to Nahms equations with a coadjoint orbit of a nilpotent element in a complex, semi-simple Lie algebra and that way equipped the orbit with an hyperkähler structure ... -
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 ... -
On the action of the group of automorphisms of the affine plane on instantons
(2011-02-09)We define an action of the group of automorphism of the affine plane on SU(2)-instantons ans investgate the orbits of this action. -
On Turing machines, groupoids, and Atiyha problem
(2011-03-17)Turing dynamical system, an abstract version of a Turing machine, is defined and investigated using groupoids. The main presented application is to the Atiyah problem in group theory. ... -
Permuting actions, moment maps and the generalized Seiberg-Witten equations
(2016-04-21)In this thesis, we study properties and the geometry related to the generalization of the Seiberg-Witten equations introduced by Taubes and Pidstrygach. A crucial ingrediant to these equations is a hyperkähler manifold M ... -
Secondary large-scale index theory and positive scalar curvature
(2016-09-06)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 large-scale (or "coarse") ...