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

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Rokhlin Invariant,, known as the Rokhlin Theorem, has played a distinguished role in the 4-dimensional topology, see [132] for a survey. Among other things, it gave rise to the Rokhlin invariant, see [75] or [146], whose properties are related to the most fundamental questions of the manifold theory, such as triangul

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Invariants of Walker and Lescop,ons were also proposed by Boyer and Lines [35] and Boyer and Nicas [36]. Walker defined his invariant by extending Casson’s .(2) intersection theory to include reducible representations, which arise as long as the first integral homology of the rational homology sphere does not vanish. Most remarkab

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Casson Invariant and Gauge Theory,t as (roughly) the Euler number of the gradient field of the Chern-Simons function. The Chern-Simons function plays a central role in modern understanding of homology 3-spheres, so we discuss it in some detail. An infinite dimensional analogue of Morse theory applied to the Chern-Simons function pro

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Instanton Floer Homology,d to as the (instanton) Floer homology. The Floer homology is an invariant of orientation preserving diffeomorphism. It is a refinement of the Casson invariant λ(.) in that λ(.) is half the Euler characteristic of ..(Σ). The definition of ..(.) relies heavily on gauge theory in dimensions three and

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978-3-642-07849-1Springer-Verlag Berlin Heidelberg 2002

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Invariants of Homology 3-Spheres978-3-662-04705-7Series ISSN 0938-0396

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https://doi.org/10.1007/978-3-662-04705-7Algebraic topology; Casson invariant; Euler characteristic; Floer homology; Gauge theory; Homotopy; Invari

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Casson Invariant,] and [275]. We first give an axiomatic definition of Casson’s invariant and prove its uniqueness and some basic properties. Then we prove existence by providing an explicit construction of λ. Deeper properties of the invariant together with some applications are described in the last three sections of this chapter.