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Seiberg-Witten invariants of non-simple type and Einstein metrics

Heberto del Rio Guerra
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Abstract

We construct examples of four dimensional manifolds with Spin$^c$-structures, whose moduli spaces of solutions to the Seiberg-Witten equations, represent a non-trivial bordism class of positive dimension, i.e. the Spin$^c$-structures are not induced by almost complex structures. As an application, we show the existence of infinitely many non-homeomorphic compact oriented 4-manifolds with free fundamental group and predetermined Euler characteristic and signature that do not carry Einstein metrics.

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Heberto del Rio Guerra. 2000-02-28. Seiberg-Witten invariants of non-simple type and Einstein metrics. https://arxiv.org/abs/math/0002243

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