# 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 Publikationsjahr 2018 Sprache Englisch Identifikator urn:nbn:de:swb:90-853639 KITopen-ID: 1000085363 Verlag Karlsruher Institut für Technologie (KIT) Umfang v, 105, VIII S. Art der Arbeit Dissertation Fakultät Fakultät für Mathematik (MATH) Institut Institut für Algebra und Geometrie (IAG) Prüfungsdatum 04.07.2018 Referent/Betreuer Prof. W. Tuschmann Schlagwörter Differential Geometry, Foliations, Global geometric and topological Methods, Classifying spaces for Foliations, Differentiable Structures, Fiber Bundles, Fiberings with Singularities, Obstruction theory
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