Periodic Monopoles and Difference Modules

This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis–Kapustin (GCK) type, and presents a classification of these monopoles in terms of difference modules with parabolic structure. It also clarifies the asymptotic behaviour of these monopoles around infinity and has applications to Yang–Mills theory and dynamical algebraic geometry.

Format: Paperback / softback
Length: 324 pages
Publication date: 24 February 2022
Publisher: Springer Nature Switzerland AG

This book delves into the realm of a specific class of monopoles, known as periodic monopoles of generalized Cherkis–Kapustin (GCK) type, which are characterized by certain mild conditions. It presents a comprehensive classification of these monopoles in terms of difference modules with parabolic structure, unveiling a fascinating Kobayashi–Hitchin correspondence between differential geometric objects and algebraic objects. Furthermore, it elucidates the asymptotic behavior of these monopoles as they approach infinity, shedding light on their mathematical properties. The theory of periodic monopoles of GCK type finds applications in both differential geometry and dynamical algebraic geometry. A thorough treatment of the theory is provided, encompassing significant generalizations of results derived from renowned mathematicians such as Charbonneau, Cherkis, Hurtubise, Kapustin, and others. Additionally, this work introduces a novel and original generalization of the nonabelian Hodge correspondence, initially studied by Corlette, Donaldson, Hitchin, and Simpson. This work is of immense interest to graduate students and researchers in differential and algebraic geometry, as well as in mathematical physics.

Weight: 528g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030944995
Edition number: 1st ed. 2022