Metrics of positive scalar curvature and generalised Morse functions, Part II
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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.References
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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
- Received by editor(s): July 18, 2011
- Published electronically: September 4, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 1-50
- MSC (2010): Primary 53C21, 57R45, 57R65; Secondary 58D17
- DOI: https://doi.org/10.1090/S0002-9947-2013-05715-7
- MathSciNet review: 3118389
Dedicated: Dedicated to Michael J. Walsh