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

• Autores: Michael Brunnbauer, Masashi Ishida, Pablo Suárez Serrato
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 16, Nº 2-3, 2009, págs. 503-514
• Idioma: inglés
• DOI: 10.4310/mrl.2009.v16.n3.a10
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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: \begin{enumerate} \item They have positive minimal volume entropy. \item They satisfy a strict version of the Gromov--Hitchin--Thorpe inequality, with a minimal volume entropy term. \item They nevertheless admit infinitely many distinct smooth structures for which no compatible Einstein metric exists. \end{enumerate}