Doubly periodic monopoles and $q$-difference modules

Abstract

An interesting theme in complex differential geometry is to find a correspondence between algebraic objects and differential geometric objects. One of the most attractive is the non-abelian Hodge theory of Simpson. In this paper, pursuing an analogue of the non-abelian Hodge theory in the context of $q$-difference modules, we study Kobayashi-Hitchin correspondences between doubly periodic monopoles and parabolic $q$-difference modules, depending on twistor parameters.

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Cited by in corpus (4)

• Exponential Networks, WKB and Topological String
• Non-Abelian Hodge Theory and Related Topics
• Triply Periodic Monopoles and Difference Modules on Elliptic Curves
• Crystal Volumes and Monopole Dynamics