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Uspekhi Mat. Nauk, 2002, Volume 57, Issue 2(344), Pages 85–138 (Mi umn497)  

This article is cited in 2 scientific papers (total in 2 papers)

Instantons and monopoles

N. A. Tyurin

Joint Institute for Nuclear Research

Abstract: In this survey we present the main notions and constructions of gauge theories, namely, the Donaldson theory, the Seiberg–Witten theory, and the theory of B-monopoles, which connects the previous two theories. In the framework of differential geometry these theories give new invariants of smooth structures in dimension 4. The introduction of these new gauge invariants has helped to solve many problems of modern geometry. The apparatus developed in the framework of these theories leads to new modern methods of investigation both in smooth geometry and in applied problems of mathematical physics. Without striving for the greatest possible generality, the survey aims to present the topic in maximal breadth and accessibility.

DOI: https://doi.org/10.4213/rm497

Full text: PDF file (548 kB)
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English version:
Russian Mathematical Surveys, 2002, 57:2, 305–360

Bibliographic databases:

UDC: 514.7
MSC: Primary 14D21, 57R57; Secondary 14J35, 81T13, 53C07, 14J80, 58E15, 14J28, 53D30
Received: 11.09.2001

Citation: N. A. Tyurin, “Instantons and monopoles”, Uspekhi Mat. Nauk, 57:2(344) (2002), 85–138; Russian Math. Surveys, 57:2 (2002), 305–360

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. A. Tyurin, “The space of Hermitian triples: local geometry”, Izv. Math., 66:4 (2002), 857–874  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. N. A. Tyurin, “Space of Hermitian Triples and Ashtekar–Isham Quantization”, Theoret. and Math. Phys., 139:1 (2004), 571–581  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
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