Einstein metrics on exotic spheres in dimensions 7, 11, and 15

Charles P. Boyer, Krzysztof Galicki, János Kollár, Evan Thomas

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

In a recent article the first three authors proved that in dimension 4m + 1 all homotopy spheres that bound parallelizable manifolds admit Einstein metrics of positive scalar curvature which, in fact, are Sasakian-Einstein. They also conjectured that all such homotopy spheres in dimension 4m−1, m ≥ 2 admit Sasakian-Einstein metrics [Boyer et al. 04], and proved this for the simplest case, namely dimension 7. In this paper we describe computer programs that show that this conjecture is also true for 11-spheres and 15-spheres. Moreover, a program is given that determines the partition of the 8,610 deformation classes of Sasakian-Einstein metrics into the 28 distinct oriented diffomorphism types in dimension 7.

Original languageEnglish (US)
Pages (from-to)59-64
Number of pages6
JournalExperimental Mathematics
Volume14
Issue number1
DOIs
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Einstein metrics
  • Exotic spheres
  • Kähler-Einstein orbifolds
  • Sasakian manifolds

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