Sökning: "Poisson manifold"
Visar resultat 1 - 5 av 7 avhandlingar innehållade orden Poisson manifold.
1. Kähler-Poisson Algebras
Sammanfattning : In this thesis, we introduce Kähler-Poisson algebras and study their basic properties. The motivation comes from differential geometry, where one can show that the Riemannian geometry of an almost Kähler manifold can be formulated in terms of the Poisson algebra of smooth functions on the manifold. LÄS MER
2. Configuration spaces, props and wheel-free deformation quantization
Sammanfattning : The main theme of this thesis is higher algebraic structures that come from operads and props.The first chapter is an introduction to the mathematical framework needed for the content of this thesis. The chapter does not contain any new results. LÄS MER
3. Prop profiles of compatible Poisson and Nijenhuis structures
Sammanfattning : A prop profile of a differential geometric structure is a minimal resolution of an algebraic prop such that representations of this resolution are in one-to-one correspondence with structures of the given type. We begin this thesis with a detailed account of the algebraic tools necessary to construct prop profiles; we treat operads and props, and resolutions of these through Koszul duality. LÄS MER
4. Going Round in Circles : From Sigma Models to Vertex Algebras and Back
Sammanfattning : In this thesis, we investigate sigma models and algebraic structures emerging from a Hamiltonian description of their dynamics, both in a classical and in a quantum setup. More specifically, we derive the phase space structures together with the Hamiltonians for the bosonic two-dimensional non-linear sigma model, and also for the N=1 and N=2 supersymmetric models. LÄS MER
5. Twisting and Gluing : On Topological Field Theories, Sigma Models and Vertex Algebras
Sammanfattning : This thesis consists of two parts, which can be read separately. In the first part we study aspects of topological field theories. We show how to topologically twist three-dimensional N=2 supersymmetric Chern-Simons theory using a contact structure on the underlying manifold. LÄS MER