Journal of the Mathematical Society of Japan

Edges, orbifolds, and Seiberg–Witten theory


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Seiberg–Witten theory is used to obtain new obstructions to the existence of Einstein metrics on 4-manifolds with conical singularities along an embedded surface. In the present article, the cone angle is required to be of the form $2\pi /p$, $p$ a positive integer, but we conjecture that similar results will also hold in greater generality.

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J. Math. Soc. Japan, Volume 67, Number 3 (2015), 979-1021.

First available in Project Euclid: 5 August 2015

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Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 57R18: Topology and geometry of orbifolds 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

Einstein metric edge-cone metric orbifold Seiberg–Witten invariant scalar curvature Weyl curvature


LEBRUN, Claude. Edges, orbifolds, and Seiberg–Witten theory. J. Math. Soc. Japan 67 (2015), no. 3, 979--1021. doi:10.2969/jmsj/06730979.

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