dc.contributor.advisor | Schick, Thomas Prof. Dr. | |
dc.contributor.author | Seyedhosseini, Mehran | |
dc.date.accessioned | 2020-07-24T12:03:49Z | |
dc.date.available | 2020-07-24T12:03:49Z | |
dc.date.issued | 2020-07-24 | |
dc.identifier.uri | http://hdl.handle.net/21.11130/00-1735-0000-0005-1434-A | |
dc.identifier.uri | http://dx.doi.org/10.53846/goediss-8119 | |
dc.language.iso | eng | de |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.subject.ddc | 510 | de |
dc.title | Index Theory and Positive Scalar Curvature | de |
dc.type | cumulativeThesis | de |
dc.contributor.referee | Schick, Thomas Prof. Dr. | |
dc.date.examination | 2019-11-14 | |
dc.description.abstracteng | 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 the higher
index of a manifold with boundary endowed with a Riemannian metric which
is collared at the boundary and has positive scalar curvature there, to the
relative higher index as defined by Chang, Weinberger and Yu. Next, we
define relative higher rho-invariants associated to positive scalar curvature
metrics on manifolds with boundary, which are collared at boundary. In
order to do this, we define variants of Roe and localisation algebras for spaces
with cylindrical ends and use this to obtain an analogue of the Higson-Roe
analytic surgery sequence for manifolds with boundary. This is followed
by a comparison of our definition of the relative index with that of Chang,
Weinberger and Yu. The higher rho-invariants can be used to classify positive
scalar curvature metrics up to concordance and bordism. In order to show
the effectiveness of the machinery developed here, we use it to give a simple
proof of the aforementioned statement regarding the relationship of indices
defined in the presence of positive scalar curvature at the boundary and the
relative higher index. We also devote a few sections to address technical
issues regarding maximal Roe and structure algebras and a maximal version
of Paschke duality, whose solutions was lacking in the literature. | de |
dc.contributor.coReferee | Meyer, Ralf Prof. Dr. | |
dc.subject.eng | Index Theory | de |
dc.subject.eng | Positive Scalar Curvature | de |
dc.identifier.urn | urn:nbn:de:gbv:7-21.11130/00-1735-0000-0005-1434-A-6 | |
dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
dc.subject.gokfull | Mathematik (PPN61756535X) | de |
dc.identifier.ppn | 1725539039 | |