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arXiv · 1803.11339

Real structures and the $\mathrm{Pin}^-(2)$-monopole equations

Nobuhiro Nakamura
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Abstract

We investigate the $\mathrm{Pin}^-(2)$-monopole invariants of symplectic $4$-manifolds and K\"{a}hler surfaces with real structures. We prove the nonvanishing theorem for real symplectic $4$-manifolds which is an analogue of Taubes' nonvanishing theorem of the Seiberg-Witten invariants for symplectic $4$-manifolds. Furthermore, the Kobayashi-Hitchin type correspondence for real K\"{a}hler surfaces is given.

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Nobuhiro Nakamura. 2018-03-30. Real structures and the $\mathrm{Pin}^-(2)$-monopole equations. https://doi.org/10.1142/s0129167x20501190

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