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Metrics of positive scalar curvature and generalised Morse functions, part I
About this Title
Mark Walsh, Mathematisches Institut, WWU Münster
Publication: Memoirs of the American Mathematical Society
Publication Year:
2011; Volume 209, Number 983
ISBNs: 978-0-8218-5304-7 (print); 978-1-4704-0597-7 (online)
DOI: https://doi.org/10.1090/S0065-9266-10-00622-8
Published electronically: June 8, 2010
Keywords: Positive scalar curvature,
Morse Theory,
surgery,
cobordism,
isotopy,
concordance
MSC: Primary 53-02, 55-02
Table of Contents
Chapters
- Introduction
- 1. Definitions and Preliminary Results
- 2. Revisiting the Surgery Theorem
- 3. Constructing Gromov-Lawson Cobordisms
- 4. Constructing Gromov-Lawson Concordances
- 5. Gromov-Lawson Concordance Implies Isotopy for Cancelling Surgeries
- 6. Gromov-Lawson Concordance Implies Isotopy in the General Case
- Appendix: Curvature Calculations from the Surgery Theorem
Abstract
It is well known that isotopic metrics of positive scalar curvature are concordant. Whether or not the converse holds is an open question, at least in dimensions greater than four. We show that for a particular type of concordance, constructed using the surgery techniques of Gromov and Lawson, this converse holds in the case of closed simply connected manifolds of dimension at least five.- Kazuo Akutagawa and Boris Botvinnik, Manifolds of positive scalar curvature and conformal cobordism theory, Math. Ann. 324 (2002), no. 4, 817–840. MR 1942251, DOI 10.1007/s00208-002-0364-y
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