Four-manifolds without Einstein metrics

Claude Lebrun

doi:10.4310/MRL.1996.v3.n2.a1

Four-manifolds without Einstein metrics

Claude Lebrun

Mathematics

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110 Scopus citations

Abstract

It is-shown that there are infinitely many compact simply connected smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2_χ > 3|τ|. The examples in question arise as non-minimal complex algebraic surfaces of general type, and the method of proof stems from Seiberg-Witten theory.

Original language	English
Pages (from-to)	133-147
Number of pages	15
Journal	Mathematical Research Letters
Volume	3
Issue number	2
DOIs	https://doi.org/10.4310/MRL.1996.v3.n2.a1
State	Published - 1996

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10.4310/MRL.1996.v3.n2.a1

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title = "Four-manifolds without Einstein metrics",

abstract = "It is-shown that there are infinitely many compact simply connected smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2χ > 3|τ|. The examples in question arise as non-minimal complex algebraic surfaces of general type, and the method of proof stems from Seiberg-Witten theory.",

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AB - It is-shown that there are infinitely many compact simply connected smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2χ > 3|τ|. The examples in question arise as non-minimal complex algebraic surfaces of general type, and the method of proof stems from Seiberg-Witten theory.

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DO - 10.4310/MRL.1996.v3.n2.a1

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SN - 1073-2780

VL - 3

SP - 133

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JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 2

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Four-manifolds without Einstein metrics

Abstract

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