Item description for Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant (De Gruyter Textbook) by Nikolai Saveliev...
Progress in low-dimensional topology has been very fast over the last two decades, leading to the solutions of many difficult problems. One of the consequences of this "acceleration of history" is that many results have only appeared in professional journals and monographs. These are hardly accessible to students who have completed only a basic course in algebraic topology, or even to some researchers whose immediate area of expertise is not topology.
Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3-spheres, as well as his l-invariant. The purpose of this book is to provide a much-needed bridge to these modern topics. The book covers some classical topics, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and gives a brief sketch of links with the latest developments in low-dimensional topology and gauge theory.
The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poncar duality on manifolds.
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Est. Packaging Dimensions: Length: 9.42" Width: 6.68" Height: 0.45" Weight: 0.8 lbs.
Publisher Walter de Gruyter
ISBN 3110162717 ISBN13 9783110162714
Reviews - What do customers think about Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant (De Gruyter Textbook)?
good book May 21, 2003
1. It is a beautiful book. There are many pictures in it. They can help you to understand concepts and proof. 2. The book begins with basic content but end with considerable deep result. Reading this book doesn¡¯t require much prior knowledge of 3-manifolds. You can read it quickly and get much. 3. The author successfully explains the Casson invariant in an elementary and readable style. He gives a short chapter to basic tools of topology. Then he describes Hergarrd splitting, Kirby moves, Dehn surgery, and intersections of 4-manifolds, Rochlin invariant, Arf invariant and representation of Lie group. At last he defines the Casson invariant and calculate some examples. 4. But there is some shortcoming. Some results are not proofed. Something needs more explanation. You can find some content is completely moved from other books. It is not natural. 5. Anymore, I recommend this book to everyone who has interest in topology. If you are no interested in topology, just read it. I bet you will start liking it.