Seiberg-Witten type equations on compact symplectic 6-manifolds

Yuuji Tanaka

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arXiv · 1407.1934

Seiberg-Witten type equations on compact symplectic 6-manifolds

Yuuji Tanaka

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Abstract

In this article, we consider a gauge-theoretic equation on compact symplectic 6-manifolds, which forms an elliptic system after gauge fixing. This can be thought of as a higher-dimensional analogue of the Seiberg-Witten equation. By using the virtual neighbourhood method by Ruan, we define an integer-valued invariant, a 6-dimensional Seiberg-Witten invariant, from the moduli space of solutions to the equations, assuming that the moduli space is compact; and it has no reducible solutions. We prove that the moduli spaces are compact if the underlying manifold is a compact Kahler threefold. We then compute the integers in some cases.

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Yuuji Tanaka. 2014-07-08. Seiberg-Witten type equations on compact symplectic 6-manifolds. https://arxiv.org/abs/1407.1934

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