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2012 | OriginalPaper | Chapter

2. Preliminaries—Fundamental Groups and Galois Groups

Author : Masanori Morishita

Published in: Knots and Primes

Publisher: Springer London

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Abstract

In this chapter we recollect the preliminary materials from topology and number theory. In particular, we give a summary about fundamental groups and Galois theory for topological spaces and arithmetic rings, together with the basic concepts and examples in 3-dimensional topology and number fields. We also review class field theory as arithmetic duality theorems in Galois, étale cohomology groups.

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previous chapter Introduction
next chapter Knots and Primes, 3-Manifolds and Number Rings
Footnotes
1
The following argument is due to S. Miyasaka, a graduate student at Kyoto University (2005).
 
2
Although the étale fundamental group is often denoted by \(\pi_{1}^{\mbox{\scriptsize\'{e}t}}(X,\overline{x})\), we write it by \(\pi _{1}(X,\overline{x})\) or π 1(X) for simplicity.
 
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Metadata
Title
Preliminaries—Fundamental Groups and Galois Groups
Author
Masanori Morishita
Copyright Year
2012
Publisher
Springer London
Book
Knots and Primes

Print ISBN: 978-1-4471-2157-2

Electronic ISBN: 978-1-4471-2158-9

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-1-4471-2158-9_2

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