Walsh, Mark (2017) Aspects of Positive Scalar Curvature and Topology I. Irish Mathematical Society Bulletin, 80. pp. 45-68. ISSN 0791-5578

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Abstract

Whether or not a smooth manifold admits a Riemannian metric whose scalar curvature function is strictly positive is a problem which has been extensively studied by geometers and topologists alike. More recently, attention has shifted to another intriguing problem. Given a smooth manifold which admits metrics of positive scalar curvature, what can we say about the topology of the space of such metrics? We provide a brief survey, aimed at the non-expert, which is intended to provide a gentle introduction to some of the work done on these deep questions.

Item Type:	Article
Keywords:	Riemannian metrics of positive scalar curvature; spin manifolds; surgery; cobordism; Morse functions; loop spaces;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	10107
Depositing User:	Mark Walsh
Date Deposited:	16 Oct 2018 14:50
Journal or Publication Title:	Irish Mathematical Society Bulletin
Publisher:	Irish Mathematical Society
Refereed:	Yes
Funders:	Simons Foundation Collaboration
URI:	https://www.maths.tcd.ie/
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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