dc.contributor.author Walsh, Mark dc.date.accessioned 2015-01-23T20:33:05Z dc.date.available 2015-01-23T20:33:05Z dc.date.issued 2014-11-12 dc.identifier.citation Walsh, Mark. The space of positive scalar curvature metrics on a manifold with boundary. arXiv:1411.2423, 2014. en_US dc.identifier.uri http://arxiv.org/abs/1411.2423 dc.identifier.uri http://hdl.handle.net/10057/11051 dc.description Preprint. Posted in arXiv en_US dc.description.abstract We study the space of Riemannian metrics with positive scalar curvature on a compact manifold with boundary. These metrics extend a fixed boundary metric and take a product structure on a collar neighbourhood of the boundary. We show that the weak homotopy type of this space is preserved by certain surgeries on the boundary in co-dimension at least three. Thus, there is a weak homotopy equivalence between the space of such metrics on a simply connected spin manifold W, of dimension n≥6 and with simply connected boundary, and the corresponding space of metrics of positive scalar curvature on the standard disk Dn. Indeed, for certain boundary metrics, this space is weakly homotopy equivalent to the space of all metrics of positive scalar curvature on the standard sphere Sn. Finally, we prove analogous results for the more general space where the boundary metric is left unfixed. en_US dc.format.extent 43 pages, 31 figures. dc.language.iso en_US en_US dc.subject Differential Geometry en_US dc.subject Algebraic Topology en_US dc.subject Space of Riemannian metrics of positive scalar curvature en_US dc.subject Manifold with boundary en_US dc.subject Surgery en_US dc.subject Bordism en_US dc.subject Spin en_US dc.subject Gromov-Lawson construction en_US dc.subject Weak homotopy equivalence en_US dc.title The space of positive scalar curvature metrics on a manifold with boundary en_US dc.type Preprint en_US
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