Galois Groups and Fundamental Groups (Cambridge Studies in Advanced Mathematics) [Hardcover]

Tamás Szamuely (Author)

Book Description

ISBN-10: 0521888506 | ISBN-13: 978-0521888509 | Publication Date: August 31, 2009 | Edition: 1

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.

Editorial Reviews

Review

"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

Book Description

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 and assuming as little technical background as possible.

See all Editorial Reviews

Product Details

• Hardcover: 280 pages
• Publisher: Cambridge University Press; 1 edition (August 31, 2009)
• Language: English
• ISBN-10: 0521888506
• ISBN-13: 978-0521888509
• Product Dimensions: 9 x 6 x 0.7 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #525,527 in Books (See Top 100 in Books)

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