Skip to main content
SpringerLink
Log in
Book cover

The Grothendieck Festschrift pp 353–373Cite as

Birkhäuser

Automorphisms of Pure Sphere Braid Groups and Galois Representations

  • Chapter
  • First Online:

Part of the book series: Modern Birkhäuser Classics ((MBC))

Abstract

Let P n be the pure braid group of the 2-sphere, with n strings (n ≥ 3), and \( \hat P_n \) be its pro-ℓ completion (ℓ: a fixed prime number). We shall study what we call the special automorphism groups of P n and \( \hat P_n \), and apply it to Galois representations of the type proposed in Grothendieck [7].

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Anderson and Y. Ihara, Pro-ℓ branched coverings ofP 1and higher circular ℓ-units, Ann. of Math. 128 (1988), 271–293.

    Article  MathSciNet  Google Scholar 

  2. M.P. Anderson, Exactness properties of profinite functors, Topology 13 (1974), 229–239.

    Article  MathSciNet  Google Scholar 

  3. J. Birman, Braids, links, and mapping class groups, Ann. of Math. Studies 82 (1975), Princeton Univ. Press.

    Google Scholar 

  4. P. Deligne, Letters to A. Grothendieck (Nov. 19, 1982, and an earlier one undated(?)), to S.Bloch (Feb. 2, March 14, 1984).

    Google Scholar 

  5. J. Dyer and E. Grossman, The automorphism groups of the braid groups, Amer. J. Math. 103 (1981), 1151–1169.

    Article  MathSciNet  Google Scholar 

  6. E. Fadell and J. Van Buskirk, The braid groups of E 2and S 2, Duke Math. J. 29 (1962), 243–257.

    Article  MathSciNet  Google Scholar 

  7. A. Grothendieck, Esquisse d’un programme, (Preprint, 1984).

    Google Scholar 

  8. Y. Ihara, Profinite braid groups, Galois representations and complex multiplications, Ann. of Math. 123 (1986), 43–106.

    Article  MathSciNet  Google Scholar 

  9. N.V. Ivanov, Algebraic properties of mapping class groups of surfaces, “Geometric and Algebraic Topology” 18 (1986), 15–35, Banach Center Publ.

    MathSciNet  Google Scholar 

  10. N. Jacobson, Lie algebras, Interscience (1962).

    Google Scholar 

  11. T. Kohno, Série de Poincaré-Koszul associée aux groupes de tresses pures, Invent. Math. 82 (1985), 57–75.

    Article  MathSciNet  Google Scholar 

  12. T. Kohno and T. Oda, The lower central series of the pure braid group of an algebraic curve, Adv. Studies in Pure Math. 12 (1987), 201–220.

    Article  MathSciNet  Google Scholar 

  13. J. McCarthy, Automorphisms of surface mapping class groups. A recent theorem of N.Ivanov, Invent. Math. 84 (1986), 49–71.

    Article  MathSciNet  Google Scholar 

  14. W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Interscience (1966).

    Google Scholar 

  15. J. Nielsen, Die Isomorphismen der allgemeinen unendlichen Gruppe mit zwei Erzeugenden, Math. Ann. 78 (1918), 385–397.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics Faculty of Science, University of Tokyo, Tokyo, 113, Japan

    Yasutaka Ihara

Authors
  1. Yasutaka Ihara
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut des Hautes Études Scientifiques, F-91440, Bures-sur-Yvette, France

    Pierre Cartier

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Nicholas M. Katz

  3. Max-Planck Institut für Mathematik, D-53111, Bonn, Germany

    Yuri I. Manin

  4. Département de Mathématiques, Université de Paris-Sud, F-91405, Orsay, France

    Luc Illusie  & Gérard Laumon  & 

  5. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Kenneth A. Ribet

Additional information

Dedicated to A. Grothendieck on his 60th birthday

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Birkhäuser Boston

About this chapter

Cite this chapter

Ihara, Y. (2007). Automorphisms of Pure Sphere Braid Groups and Galois Representations. In: Cartier, P., Katz, N.M., Manin, Y.I., Illusie, L., Laumon, G., Ribet, K.A. (eds) The Grothendieck Festschrift. Modern Birkhäuser Classics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4575-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-0-8176-4575-5_8

  • Published:

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-0-8176-4567-0

  • Online ISBN: 978-0-8176-4575-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation