Michael Brunnbauer, Masashi Ishida, Pablo Suárez-Serrato
Published 2008-07-08, updated 2008-12-18Version 2
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: 1) They have positive minimal volume entropy. 2) They satisfy a strict version of the Gromov-Hitchin-Thorpe inequality, with a minimal volume entropy term. 3) They nevertheless admit infinitely many distinct smooth structures for which no compatible Einstein metric exists.
Comments: 12 pages, v2; two references added, to appear in Math. Research Letters
Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds
On the nonexistence of Einstein metric on 4-manifolds
Einstein metrics on connected sums of $S^2\times S^3$
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