منابع مشابه
Unitary Representations of Brieskorn Spheres
In this article, we commence an investigation of the SU(N) representation space of Seifert bered homology spheres (a 1 ; : : : ; a n): Under mild assumptions (e.g. if N is prime), then Theorem 3.1 implies that any closed connected component of irreducible SU(N) representations of (a 1 ; : : : ; a n) is homeomorphic to a component of SU(N) representations of an associated genus zero Fuchsian gro...
متن کاملLattice Points Inside Rational Simplices and the Casson Invariant of Brieskorn Spheres
From the very beginning, it was apparent that the Seiberg^Witten analogue of the instanton Floer homology of a (Z-)homology 3-sphere is no longer a topological invariant, since it can vary with the metric. W. Chen [2], Y. Lim [7] and Marcolli^Wang [8] have explained the metric dependence of the Euler characteristic of the SWF (1⁄4 Seiberg^Witten^Floer) homology. More precisely, if gi ði 1⁄4 0; ...
متن کاملFloer 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...
متن کاملOn the Quantum Invariant for the Brieskorn Homology Spheres
We study an exact asymptotic behavior of the Witten–Reshetikhin–Turaev invariant for the Brieskorn homology spheres Σ(p1, p2, p3) by use of properties of the modular form following a method proposed by R. Lawrence and D. Zagier. Key observation is that the invariant coincides with a limiting value of the Eichler integral of the modular form with weight 3/2. We show that the Casson invariant is ...
متن کاملFloer Homology of Brieskorn Homology Spheres : Solution to Atiyah’s Problem
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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13828