Spin Manifolds, Einstein Metrics, and Differential Topology

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dc.creatorIshida, Masashi
dc.creatorLeBrun, Claude
dc.date2001-07-16
dc.date2001-10-31
dc.date.accessioned2026-07-07T04:42:37Z
dc.date.available2026-07-07T04:42:37Z
dc.descriptionWe show that there exist smooth, simply connected, four-dimensional spin manifolds which do not admit Einstein metrics, but nonetheless satisfy the strict Hitchin-Thorpe inequality. Our construction makes use of the Bauer/Furuta cohomotopy refinement of the Seiberg-Witten invariant, in conjunction with curvature estimates previously proved by the second author. These methods also easily allow one to construct examples of topological 4-manifolds which admit an Einstein metric for one smooth structure, but which have infinitely many other smooth structures for which no Einstein metric can exist.
dc.description17 pages, LaTeX2e; minor errors corrected; references added
dc.identifierhttps://arxiv.org/abs/math/0107111
dc.identifierhttp://arxiv.org/abs/math/0107111
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61856
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject53C25; 57R57
dc.titleSpin Manifolds, Einstein Metrics, and Differential Topology
dc.typetext

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