An essential relation between einstein metrics, volume entropy, and exotic smooth structures

Michael Brunnbauer, Masashi Ishida, Pablo Suárez-Serrato

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We show that the minimal volume entropy of closed manifolds remains unaffected when nonessential manifolds are added in a connected sum. We combine this result with the stable cohomotopy invariant of Bauer-Furuta in order to present an infinite family of four-manifolds with the following properties: (i) They have positive minimal volume entropy. (ii) They satisfy a strict version of the Gromov-Hitchin-Thorpe inequality, with a minimal volume entropy term. (iii) They nevertheless admit infinitely many distinct smooth structures for which no compatible Einstein metric exists.

Original languageEnglish
Pages (from-to)503-514
Number of pages12
JournalMathematical Research Letters
Volume16
Issue number3
DOIs
Publication statusPublished - 2009 May

Keywords

  • Einstein metrics
  • Exotic smooth structures
  • Gromov-hitchin-thorpe inequality
  • Minimal volume entropy
  • Seiberg-witten invariants

ASJC Scopus subject areas

  • Mathematics(all)

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