Existence of mASD connections on 4-manifolds with cylindrical ends
David L. Duncan, Ian Hambleton
TL;DR
This paper extends Taubes' gluing theorems to establish the existence of mASD connections on 4-manifolds with cylindrical ends, including cases with degenerate asymptotic flat connections.
Contribution
It generalizes existing ASD connection existence results to manifolds with cylindrical ends and degenerate asymptotic conditions.
Findings
Extended gluing theorems to cylindrical end manifolds
Proved existence of mASD connections under new conditions
Applied results to degenerate asymptotic flat connections
Abstract
Taubes' gluing theorems establish the existence of ASD connections on closed, oriented 4-manifolds. We extend these gluing results to the mASD connections of Morgan-Mrowka-Ruberman on oriented 4-manifolds with cylindrical ends. As a corollary, we obtain an ASD-existence result in the presence of degenerate asymptotic flat connections.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals