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Nikolai Saveliev, "Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant"

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 Poncaré duality on manifolds.

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	Science/Engineering Topology of Manifolds R. L. Wilder, "Topology of Manifolds" American Mathematical Society; 4th edition (December 31, 1949) \| ISBN-10: 0821810324 \| 403 Pages \| Djvu \| 30,6 MB This book is a standard in this area of mathematics and is invaluable for historical ba ...
	Study Invariant Forms on Grassmann Manifolds, Vol. 89 (Annals of Mathematics Studies) Wilhelm Stoll "Invariant Forms on Grassmann Manifolds, Vol. 89 (Annals of Mathematics Studies)"Princeton University Press \| English \| 1978-01-01 \| ISBN: 0691081999 \| 128 pages \| DJVU \| 1,1 MBMost of the results in this monograph are known. ...
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	Topology of Surfaces, Knots, and Manifolds Topology of Surfaces, Knots, and Manifolds: Stephan C. CarlsonWiley \| ISBN: 0471355445 \| 2001-01-01 \| djvu (ocr) \| 176 pages \| 17.16 MbTopology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the b ...

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