Local mean dimension of ASD moduli spaces over the cylinder

TL;DR

This paper investigates the local mean dimension of an infinite-dimensional anti-self-dual (ASD) moduli space over the cylinder, introducing non-degenerate ASD connections and their deformation theory to compute this dimension.

Contribution

It develops the deformation theory of non-degenerate ASD connections and provides a formula for the local mean dimension of the moduli space.

Findings

Derived a formula for the local mean dimension of the ASD moduli space.

Established the existence of many non-degenerate ASD connections via gluing methods.

Enhanced understanding of the structure of ASD moduli spaces over cylinders.

Abstract

We study an infinite dimensional ASD moduli space over the cylinder. Our main result is the formula of its local mean dimension. A key ingredient of the argument is the notion of non-degenerate ASD connections. We develop its deformation theory and show that there exist sufficiently many non-degenerate ASD connections by using the method of gluing infinitely many instantons.