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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Metrics of positive scalar curvature and generalised Morse functions, Part II


Author: Mark Walsh
Journal: Trans. Amer. Math. Soc. 366 (2014), 1-50
MSC (2010): Primary 53C21, 57R45, 57R65; Secondary 58D17
Published electronically: September 4, 2013
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Abstract: The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli spaces. In this paper, we extend this technique to work for families of generalised Morse functions, i.e. smooth functions with both Morse and birth-death singularities.


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Additional Information

Mark Walsh
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
Address at time of publication: Department of Mathematics, Statistics and Physics, Wichita State University, Wichita, Kansas 67260
Email: walsh@math.wichita.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05715-7
PII: S 0002-9947(2013)05715-7
Received by editor(s): July 18, 2011
Published electronically: September 4, 2013
Dedicated: Dedicated to Michael J. Walsh
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.