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Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I
Mark Walsh, Westfälische Wilhelms-Universität Münster, Germany
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Memoirs of the American Mathematical Society
2011; 80 pp; softcover
Volume: 209
ISBN-10: 0-8218-5304-X
ISBN-13: 978-0-8218-5304-7
List Price: US$69
Individual Members: US$41.40
Institutional Members: US$55.20
Order Code: MEMO/209/983
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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. The author shows 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.

Table of Contents

  • Definitions and preliminary results
  • Revisiting the surgery theorem
  • Constructing Gromov-Lawson cobordisms
  • Constructing Gromov-Lawson concordances
  • Gromov-Lawson concordance implies isotopy for cancelling surgeries
  • Gromov-Lawson concordance implies isotopy in the general case
  • Appendix: Curvature calculations from the surgery theorem
  • Bibliography
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