Deformation theory of asymptotically conical coassociative 4‐folds
Deformation theory of asymptotically conical coassociative 4‐folds
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渐近圆锥共结合四重变形理论
DOI：
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发表时间：
2004
期刊：
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通讯作者：
Jason D. Lotay
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文献类型：
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作者：
Jason D. Lotay
假设一个协合的4 -叠N在一个速率λ < 1的锥C上是渐近圆锥（AC）。如果λ∈[−2,1)是泛型的，则证明了速率为λ的N的AC到C的协结合变形的模空间是光滑流形，并计算了其维数。如果λ <−2且为泛型，则证明了模空间局部同胚于光滑流形间光滑映射的核，并给出了其期望维数的下界。我们还推导了当λ < - 2时N是平面的一个检验，并讨论了AC协缔4 -折叠的例子。
Suppose that a coassociative 4‐fold N in ℝ7 is asymptotically conical (AC) to a cone C with rate λ < 1. If λ ∈ [−2, 1) is generic, then we show that the moduli space of coassociative deformations of N that are also AC to C with rate λ is a smooth manifold, and we calculate its dimension. If λ < − 2 and generic, then we show that the moduli space is locally homeomorphic to the kernel of a smooth map between smooth manifolds, and we give a lower bound for its expected dimension. We also derive a test for when N will be planar if λ < − 2 and we discuss examples of AC coassociative 4‐folds.