论文标题
扭曲连接的sum $ g_2 $ -manifolds
Associative submanifolds in twisted connected sum $G_2$-manifolds
论文作者
论文摘要
我们介绍了一种方法，以在扭曲的连接sum $ g_2 $ -manifolds中构造封闭的刚性关联子曼if。更准确地说，我们证明了在假设下酰基$ g_2 $ manifolds中渐近圆柱（酰基）关联亚策略的胶合定理。这类似于[SW15]中引入的$ g_2 $ -instantons的胶合定理。在特殊情况下，我们重述了酰基缔合子曼膜的假设，该假设是从holomorphic曲线或酰基calabi-yau的特殊Lagrangians获得的3美元。通过这种方式，我们找到了许多新的关联子手机，它们差异为$ s^3 $，$ \ MATHBF R \ MATHBF P^3 $或$ \ MATHBF R \ MATHBF P^3 \＃\ MATHBF R \ MATHBF R \ MATHBF P^3 $。
We introduce a method to construct closed rigid associative submanifolds in twisted connected sum $G_2$-manifolds. More precisely, we prove a gluing theorem of asymptotically cylindrical (ACyl) associative submanifolds in ACyl $G_2$-manifolds under a hypothesis. This is analogous to the gluing theorem for $G_2$-instantons introduced in [SW15]. We rephrase the hypothesis in the special cases where the ACyl associative submanifolds are obtained from holomorphic curves or special Lagrangians in ACyl Calabi-Yau $3$-folds. In this way we find many new associative submanifolds which are diffeomorphic to $S^3$, $\mathbf R\mathbf P^3$ or $\mathbf R\mathbf P^3\#\mathbf R\mathbf P^3$.
