Title: Complex $G_2$-manifolds and Seiberg-Witten Equations
Abstract: We introduce the notion of complex $G_2$ manifold $M_{\mathbb C}$, and complexification of a $G_2$ manifold $M\subset M_{\mathbb C}$. As an application we show the following: If $(Y,s)$ is a closed oriented $3$-manifold with a $Spin^{c}$ structure, and $(Y,s)\subset (M, \varphi)$ is an imbedding as an associative submanifold of some $G_2$ manifold (such imbedding always exists), then the isotropic associative deformations of $Y$ in the complexified $G_2$ manifold $M_{\mathbb C}$ is given by Seiberg-Witten equations.
Publication Year: 2018
Publication Date: 2018-04-26
Language: en
Type: preprint
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