Spin manifolds, Einstein metrics, and differential topology

Masashi Ishida, Claude LeBrun

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We show that there exist smooth, simply connected, four-dimensional spin manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality. Our construction makes use of the Bauer/Furuta cohomotopy refinement of the Seiberg-Witten invariant, in conjunction with curvature estimates previously proved by the second author. These methods also allow one to easily construct many examples of topological 4-manifolds which admit an Einstein metric for one smooth structure, but which have infinitely many other smooth structures for which no Einstein metric can exist.

Original languageEnglish
Pages (from-to)229-240
Number of pages12
JournalMathematical Research Letters
Issue number2-3
Publication statusPublished - 2002
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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