TY - JOUR
T1 - Instanton approximation, periodic ASD connections, and mean dimension
AU - Matsuo, Shinichiroh
AU - Tsukamoto, Masaki
N1 - Funding Information:
✩ Shinichiroh Matsuo was supported by Grant-in-Aid for JSPS fellows (19·5618) from JSPS, and Masaki Tsukamoto was supported by Grant-in-Aid for Young Scientists (B) (21740048) from MEXT. * Corresponding author. E-mail addresses: exotic@ms.u-tokyo.ac.jp (S. Matsuo), tukamoto@math.kyoto-u.ac.jp (M. Tsukamoto).
PY - 2011/3/1
Y1 - 2011/3/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jfa.2010.11.008
DO - 10.1016/j.jfa.2010.11.008
M3 - Article
AN - SCOPUS:78650555075
SN - 0022-1236
VL - 260
SP - 1369
EP - 1427
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 5
ER -