ON THE QUANTUM INVARIANT FOR THE BRIESKORN HOMOLOGY SPHERES
نویسندگان
چکیده
منابع مشابه
On 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 ...
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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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In this paper, we give a parameterization of the SU(2, 1) representation space of the Brieskorn homology spheres using the trace coordinates. As applications, we give an example which shows that the orbifold Toledo invariant in [10] does not distinguish the connected components of the PU(2, 1) representation space.
متن کاملContact Homology of Brieskorn Manifolds
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: International Journal of Mathematics
سال: 2005
ISSN: 0129-167X,1793-6519
DOI: 10.1142/s0129167x05003004