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Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant
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Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant Hardback - 2011

by Nikolai Saveliev

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From the publisher

Progress in low-dimensional topology has been very quick in the last three decades, leading to the solutions of many difficult problems. Among the earlier highlights of this period was Casson's λ-invariant that was instrumental in proving the vanishing of the Rohlin invariant of homotopy 3-spheres. The proof of the three-dimensional Poincar conjecture has rendered this application moot but hardly made Casson's contribution less relevant: in fact, a lot of modern day topology, including a multitude of Floer homology theories, can be traced back to his λ-invariant.

The principal goal of this book, now in its second revised edition, remains providing an introduction to the low-dimensional topology and Casson's theory; it also reaches out, when appropriate, to more recent research topics. The book covers some classical material, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It then proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and concludes with a brief overview of recent developments.

The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic and differential topology, including the fundamental group, basic homology theory, transversality, and Poincar duality on manifolds.

Details

  • Title Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant
  • Author Nikolai Saveliev
  • Binding Hardback
  • Edition 2 Revised
  • Pages 218
  • Volumes 1
  • Language ENG
  • Publisher de Gruyter
  • Publication date 2011-12-19
  • Features Bibliography, Glossary, Index
  • ISBN 9783110250350 / 3110250357
  • Weight 0.8 lbs (0.36 kg)
  • Dimensions 9.3 x 6.7 x 0.5 in (23.62 x 17.02 x 1.27 cm)
  • Age range 18 to 21 years
  • Grade levels 13 - 16
  • Themes
    • Aspects (Academic): Science/Technology Aspects
  • Category Mathematics
  • Library of Congress subjects Three-manifolds (Topology)
  • Library of Congress Catalogue Number 2011037009
  • Dewey Decimal Code 514.34

Media reviews

Citations

  • Reference and Research Bk News, 04/01/2012, Page 204

About the author

Nikolai Saveliev, University of Miami, Florida, USA.

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