Instanton approximation, periodic ASD connections, and mean dimension

Details Instanton approximation, periodic ASD connections, and mean dimension Instanton approximation, periodic ASD connections, and mean dimension

2009-09-07

arxiv.org/abs/0909.1141v1

Mathematics

Differential Geometry

55 pages

Scientific paper

We study a moduli space of ASD connections over $S^3\times \mathbb{R}$. 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.

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