Local mean dimension of ASD moduli spaces over the cylinder

2013/02/25 by Matsuo, Shinichiroh, Tsukamoto, Masaki
#53C07 #58D27 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1302.5977

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.

Related

• Instanton approximation, periodic ASD connections, and mean dimension
• Local Nahm transform and singularity formation of ASD connections
• Sharp lower bound on the curvatures of ASD connections over the cylinder
• Dimension Reduction of Generalized ASD Instantons
• Large dynamics of Yang--Mills theory: mean dimension formula