Manifolds with aspherical singular Riemannian foliations

Corro Tapia, Diego

Abstract (englisch):
In the present work we study $A$-foliations, i.e. singular Riemannian foliations with regular leaf aspherical. The main result is that, for a simply-connected closed $(n+2)$-manifold $M$, an $A$-foliation with regular leaves of codimension $2$ in $M$ is homogeneous. In other words it is given by a smooth effective action of the torus $\mathbb{T }^n$ on $M$ by isometries.

We will give some conditions to compare two simply-connected, closed manifolds with $A$-foliations, up to foliated homeomorphism, via their leaf spaces.

 Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG) Publikationstyp Hochschulschrift Jahr 2018 Sprache Englisch Identifikator URN: urn:nbn:de:swb:90-853639 KITopen ID: 1000085363 Verlag Karlsruhe Umfang v, 105, VIII S. Abschlussart Dissertation Fakultät Fakultät für Mathematik (MATH) Institut Institut für Algebra und Geometrie (IAG) Prüfungsdatum 04.07.2018 Referent/Betreuer Prof. W. Tuschmann Schlagworte Differential Geometry, Foliations, Global geometric and topological Methods, Classifying spaces for Foliations, Differentiable Structures, Fiber Bundles, Fiberings with Singularities, Obstruction theory
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft KITopen Landing Page