By Nikolai Saveliev
Growth in low-dimensional topology has been very fast within the final 3 a long time, resulting in the options of many tricky difficulties. one of the past highlights of this era used to be Casson's -invariant that was once instrumental in proving the vanishing of the Rohlin invariant of homotopy 3-spheres. The evidence of the third-dimensional Poincare conjecture has rendered this software moot yet not often made Casson's contribution much less suitable: in reality, loads of modern-day topology, together with a large number of Floer homology theories, may be traced again to his -invariant. The imperative aim of this ebook, now in its moment revised version, is still supplying an creation to the low-dimensional topology and Casson's idea; it additionally reaches out, whilst acceptable, to newer examine issues. The e-book covers a few classical fabric, comparable to Heegaard splittings, Dehn surgical procedure, and invariants of knots and hyperlinks. It then proceeds during the Kirby calculus and Rohlin's theorem to Casson's invariant and its purposes, and concludes with a quick evaluate of contemporary advancements. The booklet can be obtainable to graduate scholars in arithmetic and theoretical physics acquainted with a few effortless algebraic and differential topology, together with the basic crew, easy homology idea, transversality, and Poincare duality on manifolds.
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