Titlebook: Invariants of Homology 3-Spheres; Nikolai Saveliev Book 2002 Springer-Verlag Berlin Heidelberg 2002 Algebraic topology.Casson invariant.Eu

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Nikolai SavelievGuide book with many new results on major topics in topology.Includes supplementary material:

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Homology 3-Spheres,6] and [222]. Therefore, we can work in all three categories interchangeably. Usually, ℤ-homology spheres are referred to as ., and ℚ-homology spheres as .. Homology 3-spheres exist in abundance. We begin with some examples and constructions.

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The Homology Cobordism Group,π;.(.) = 0, only that ..(., ℤ) = 0. A homology sphere . is said to be . if it is homology cobordant to .. or, equivalently, bounds a smooth acyclic 4-manifold. Note that the requirement that the homology cobordism be . is essential — it is known [98] that any integral homology 3-sphere bounds a . compact oriented 4-manifold which is acyclic.

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0938-0396 nifold whose homology equals that of the 3-sphere. These objects may look rather special but they have played an outstanding role in geometric topology for the past fifty years. The book gives a systematic exposition of diverse ideas and methods in the area, from algebraic topology of manifolds to i

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Casson Invariant and Gauge Theory,. Herald. Another one is the Casson-type invariant for knots in integral homology spheres introduced by X.-S. Lin and C. Herald, and finally, the equivariant Casson invariant of integral homology spheres with a finite cyclic group action by O. Collin and the author.

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Book 2002layed an outstanding role in geometric topology for the past fifty years. The book gives a systematic exposition of diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered are constructions and classificat