Abstract
AbstractWe exhibit the first examples of closed 7-dimensional Riemannian manifolds with holonomy $$G_2$$
G
2
that are homeomorphic but not diffeomorphic. These are also the first examples of closed Ricci-flat manifolds that are homeomorphic but not diffeomorphic. The examples are generated by applying the twisted connected sum construction to Fano 3-folds of Picard rank 1 and 2. The smooth structures are distinguished by the generalised Eells–Kuiper invariant introduced by the authors in a previous paper.
Funder
Simons Foundation
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference43 articles.
1. Baraglia, D.: $${G}_2$$ geometry and integrable systems, Ph.D. thesis, University of Oxford (2009). arXiv:1002.1767
2. Beauville, A.: Fano Threefolds and K3 Surfaces, The Fano Conference, pp. 175–184. Univ. Torino, Turin (2004)
3. Berger, M.: Sur les groupes d’holonomie homogène des variétés à connexion affines et des variétés riemanniennes. Bull. Soc. Math. Fr. 83, 279–330 (1955)
4. Blanc, J., Lamy, S.: Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links. Proc. Lond. Math. Soc. 105, 1047–1075 (2012)
5. Bonan, E.: Sur les variétés riemanniennes à groupe d’holonomie $${G}_2$$ ou $${S}pin(7)$$. C. R. Acad. Sci. Paris 262, 127–129 (1966)
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