Periodic Monopoles and Difference Modules

Takuro Mochizuki (Autor)

Buch | Softcover

XVIII, 324 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-030-94499-5 (ISBN)

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This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis-Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi-Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity.
The theory of periodic monopoles of GCK type has applications to Yang-Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson.
This work will be of interest to graduatestudents and researchers in differential and algebraic geometry, as well as in mathematical physics.

lt;b>Takuro Mochizuki has been awarded the 2022 Breakthrough Prize in Mathematics for advancing the understanding of holonomic D-modules through his research on harmonic bundles and twister D-modules, which he has studied at the "interface of algebraic geometry and differential geometry".

. - Introduction. - Preliminaries. - Formal Difference Modules and Good Parabolic Structure. - Filtered Bundles. - Basic Examples of Monopoles Around Infinity. - Asymptotic Behaviour of Periodic Monopoles Around Infinity. - The Filtered Bundles Associated with Periodic Monopoles. - Global Periodic Monopoles of Rank One. - Global Periodic Monopoles and Filtered Difference Modules. - Asymptotic Harmonic Bundles and Asymptotic Doubly Periodic Instantons (Appendix).

Erscheinungsdatum	26.02.2022
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XVIII, 324 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	524 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Naturwissenschaften ► Physik / Astronomie
Schlagworte	-Connections • DifferenceModule • Kobayashi-Hitchin Correspondence • Monopole • Parabolic Structure • λ-Connections
ISBN-10	3-030-94499-9 / 3030944999
ISBN-13	978-3-030-94499-5 / 9783030944995
Zustand	Neuware