An essential relation between Einstein metrics, volume entropy, and exotic smooth structures
Differential Geometry
2022-02-15 v2 Geometric Topology
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: 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.
Cite
@article{arxiv.0807.1187,
title = {An essential relation between Einstein metrics, volume entropy, and exotic smooth structures},
author = {Michael Brunnbauer and Masashi Ishida and Pablo Suárez-Serrato},
journal= {arXiv preprint arXiv:0807.1187},
year = {2022}
}
Comments
12 pages, v2; two references added, to appear in Math. Research Letters