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

Michael Brunnbauer, Masashi Ishida, Pablo Suárez-Serrato

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)503-514
ページ数12
ジャーナルMathematical Research Letters
16
3
DOI
出版ステータスPublished - 2009 5月

ASJC Scopus subject areas

  • 数学 (全般)

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