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Link Groups and Galois Groups with Restricted Ramification

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Knots and Primes

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Abstract

In this chapter we discuss the analogy between Galois groups with restricted ramification and link groups. In particular, we shall see the close analogy between Milnor’s theorem on the structure of a link group and a theorem by H. Koch on the structure of a pro-l Galois group over the rational number field with restricted ramification.

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References

  1. Birman, J.: Braids, Links, and Mapping Class Groups. Annals of Mathematics Studies, vol. 82. Princeton Univ. Press/Univ. of Tokyo Press, Princeton/Tokyo (1974)

    Google Scholar 

  2. Hillman, J., Matei, D., Morishita, M.: Pro-p link groups and p-homology groups. In: Primes and Knots. Contemporary Mathematics, vol. 416, pp. 121–136. Am. Math. Soc., Providence (2006)

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  3. Koch, H.: On p-extensions with given ramification, Appendix 1. In: [Hb], pp. 89–126

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  4. Labute, J.: Mild pro-p-groups and Galois groups of p-extensions of \(\textbf{Q}\). J. Reine Angew. Math. 596, 155–182 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Labute, J., Mináč, J.: Mild pro-2-groups and 2-extensions of ℚ with restricted ramification. J. Algebra 332, 136–158 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Milnor, J.: Isotopy of links. In: Fox, R.H., Spencer, D.S., Tucker, W. (eds.) Algebraic Geometry and Topology, pp. 280–306. Princeton Univ. Press, Princeton (1957). A Symposium in Honour of S. Lefschetz

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  7. Schmidt, A.: Circular sets of prime numbers and p-extensions of the rationals. J. Reine Angew. Math. 596, 115–130 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Stallings, J.: Homology and central series of groups. J. Algebra 2, 170–181 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  9. Turaev, V.G.: Milnor’s invariants and Massey products. J. Sov. Math. 12, 128–137 (1979) (English transl.)

    Article  MATH  Google Scholar 

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Correspondence to Masanori Morishita .

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Morishita, M. (2012). Link Groups and Galois Groups with Restricted Ramification. In: Knots and Primes. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-2158-9_7

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