Floer homology of Brieskorn homology spheres
نویسندگان
چکیده
منابع مشابه
Floer Homology of Brieskorn Homology Spheres
Every Brieskorn homology sphere (p; q; r) is a double cover of the 3{sphere ramiied over a Montesinos knot k(p; q; r). We relate Floer homology of (p; q; r) to certain invariants of the knot k(p; q; r), among which are the knot signature and the Jones polynomial. We also deene an integer valued invariant of integral homology 3{spheres which agrees with the {invariant of W. Neu-mann and L. Siebe...
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In this paper we answer the question posed by M. Atiyah, see [12], and give an explicit formula for Floer homology of Brieskorn homology spheres in terms of their branching sets over the 3–sphere. We further show how Floer homology is related to other invariants of knots and 3–manifolds, among which are the μ̄–invariant of W. Neumann and L. Siebenmann and the Jones polynomial. Essential progress...
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Heegaard Floer homology was introduced by Ozsváth and Szabó [16]. For nullhomologous knots, there is a filtered version of Heegaard Floer homology, called knot Floer homology; see Ozsváth and Szabó [14] and Rasmussen [18]. Basically, if one knows the information about the knot Floer homology of a knot, then one can compute the Heegaard Floer homology of any manifold obtained by Dehn surgery on ...
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We give an algorithm for computing the contact homology of some Brieskorn manifolds. As an application, we construct infinitely many contact structures on the class of simply connected contact manifolds that admit nice contact forms (i.e. no Reeb orbits of degree -1,0 or 1) and have index positivity with trivial first Chern class.
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1999
ISSN: 0022-040X
DOI: 10.4310/jdg/1214425447