Instanton approximation, periodic ASD connections, and mean dimension
Instanton approximation, periodic ASD connections, and mean dimension
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DOI：
10.1016/j.jfa.2010.11.008
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发表时间：
2009-09
影响因子：
1.7
通讯作者：
Shinichiroh Matsuo;M. Tsukamoto
中科院分区：
文献类型：
--
作者：
Shinichiroh Matsuo;M. Tsukamoto
我们研究了S3×R上ASD联络的模空间，我们不仅考虑了有限能量的ASD联络，而且还考虑了无限能量的ASD联络。所以模空间一般是无限维的。我们研究了这个无限维模空间的(局部)平均维度。通过构造周期ASD连接的无限维形变理论，我们用“龙格近似”证明了ASD连接的平均维上界.
We study a moduli space of ASD connections over S3×R. We consider not only finite energy ASD connections but also infinite energy ones. So the moduli space is infinite dimensional in general. We study the (local) mean dimension of this infinite dimensional moduli space. We show the upper bound on the mean dimension by using a “Runge-approximation” for ASD connections, and we prove its lower bound by constructing an infinite dimensional deformation theory of periodic ASD connections.