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Galois Groups and Fundamental Groups

$69.99

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: August 2009
  • availability: In stock
  • format: Hardback
  • isbn: 9780521888509

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  • Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.

    • Provides key applications and recent results throughout
    • A friendly introduction to material that isn't usually taught until advanced graduate level
    • Class tested by the author with graduate and advanced undergraduate students
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    Reviews & endorsements

    "The book is well written and contains much information about the etale fundamental group. There are exercises in every chapter. On the whole, the book is useful for mathematicians and graduate students looking for one place where they can find information about the etale fundamental group and the related Nori fundamental group scheme."
    Swaminathan Subramanian, Mathematical Reviews

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    Product details

    • Date Published: August 2009
    • format: Hardback
    • isbn: 9780521888509
    • length: 280 pages
    • dimensions: 235 x 155 x 19 mm
    • weight: 0.52kg
    • contains: 60 exercises
    • availability: In stock
  • Table of Contents

    Foreword
    1. Galois theory of fields
    2. Fundamental groups in topology
    3. Riemann surfaces
    4. Fundamental groups of algebraic curves
    5. Fundamental groups of schemes
    6. Tannakian fundamental groups
    Bibliography
    Index.

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    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

    If you are having problems accessing these resources please email cflack@cambridge.org

  • Author

    Tamás Szamuely, Hungarian Academy of Sciences, Budapest
    Tamás Szamuely is a Senior Research Fellow in the Alfréd Rényi Institute of Mathematics at the Hungarian Academy of Sciences, Budapest.

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