Global ETD Search

131	Symmetric Squaring in Homology and Bordism / Symmetrisches Quadrieren in Homologie und Bordismus Krempasky, Seyide Denise 25 August 2011 (has links) Betrachtet man das kartesische Produkt X × X eines topologischen Raumes X mit sich selbst, so kann auf diesem Objekt insbesondere die Involution betrachtet werden, die die Koordinaten vertauscht, die also (x,y) auf (y,x) abbildet. Das sogenannte 'Symmetrische Quadrieren' in Čech-Homologie mit Z/2-coefficients wurde von Schick et al. 2007 als Abbildung von der k-ten Čech-Homologiegruppe eines Raumes X in die 2k-te Čech-Homologiegruppe von X × X modulu der oben genannten Involution definiert. Es stellt sich heraus, dass diese Konstruktion entscheidend ist für den Beweis eines parametrisierten Borsuk-Ulam-Theorems.Das Symmetrische Quadrieren kann zu einer Abbildung in Bordismus verallgemeinert werden, was der Hauptgegenstand dieser Dissertation ist. Genauer gesagt werden wir zeigen, dass es eine wohldefinierte, natürliche Abbildung von der k-ten singulären Bordismusgruppe von X in die 2k-te Bordismusgruppe von X × X modulu der obigen Involution gibt.Insbesondere ist dieses Quadrieren wirklich eine Verallgemeinerung der Konstruktion in Čech-Homologie, denn es ist vertauschbar mit dem Übergang von Bordismus zu Homologie via dem Fundamentalklassenhomomorphismus. Auf dem Weg zu diesem Resultat wird das Konzept des Čech-Bordismus als Kombination aus Bordismus und Čech-Homologie zunächst definiert und dann mit Čech-Homologie verglichen. 510 Mathematik Mathematics and Computer Science Algebraische Topologie Homologietheorie Bordismus Čech homology algebraic topology homology theory bordism Čech homology 31.60 31.69 EFHQ 200
132	Cohomologies on sympletic quotients of locally Euclidean Frolicher spaces Tshilombo, Mukinayi Hermenegilde 08 1900 (has links) This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies. Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures. / Mathematical Sciences / D. Phil. (Mathematics) Constant dimension Locally Euclidean Frolicher spaces Symplectic structure Symplectic geometry Symplectic quotient or reduced space Exterior algebra Ringed Frolicher space Smooth Gelfand representation Sheaf cohomology Alexander-Spanier cohomology Singular cohomology Cech cohomology and de Rham cohomology Vector fields and mechanics 514.224 Homology theory Symplectic manifolds Topological spaces Sheaf theory Geometry, Differential Hamiltonian graph theory Algebraic spaces
133	Thetafunktionen und konjugationsinvariante Funktionen auf Paaren von Matrizen / Theta functions and conjugation invariant functions on pairs of matrices Eickhoff-Schachtebeck, Annika 30 September 2008 (has links) No description available. 510 Mathematik Mathematics and Computer Science Paare von Matrizen Thetafunktionen Painleve-Analysis integrable Systeme Spektralkurve pairs of matrices theta functions painleve analysis integrable systems spectral curves 31.51 EBEF 050: Vector bundles sheaves
134	Cohomologies on sympletic quotients of locally Euclidean Frolicher spaces Tshilombo, Mukinayi Hermenegilde 08 1900 (has links) This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies. Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures. / Mathematical Sciences / D. Phil. (Mathematics) Constant dimension Locally Euclidean Frolicher spaces Symplectic structure Symplectic geometry Symplectic quotient or reduced space Exterior algebra Ringed Frolicher space Smooth Gelfand representation Sheaf cohomology Alexander-Spanier cohomology Singular cohomology Cech cohomology and de Rham cohomology Vector fields and mechanics 514.224 Homology theory Symplectic manifolds Topological spaces Sheaf theory Geometry, Differential Hamiltonian graph theory Algebraic spaces

Page generated in 0.0583 seconds