The Sl2(c) Casson Invariant for Seifert Fibered Homology Spheres and Surgeries on Twist Knots
نویسنده
چکیده
We derive a simple closed formula for the SL2(C) Casson invariant for Seifert fibered homology 3-spheres using the correspondence between SL2(C) character varieties and moduli spaces of parabolic Higgs bundles of rank two. These results are then used to deduce the invariant for Dehn surgeries on twist knots by combining computations of the Culler-Shalen norms with the surgery formula for the SL2(C) Casson invariant.
منابع مشابه
On Heegaard Floer Homology and Seifert Fibered Surgeries
We explore certain restrictions on knots in the three-sphere which admit non-trivial Seifert fibered surgeries. These restrictions stem from the Heegaard Floer homology (defined in [8]) for Seifert fibered spaces (compare [11]), and hence they have consequences for both the Alexander polynomial of such knots, and also their “knot Floer homology” (introduced in [10]). In particular, it is shown ...
متن کاملRational Surgery Formula for Habiro–le Invariants of Rational Homology 3–spheres
Habiro–Le invariants dominate sl2 Witten–Reshetikhin–Turaev invariants of rational homology 3–spheres at roots of unity of order coprime with the torsion. In this paper we give a formula for the Habiro–Le invariant of a rational homology 3–sphere obtained by rational surgery on a link in S. As an application, we compute this invariant for Seifert fibered spaces and for Dehn surgeries on twist k...
متن کاملSeifert fibered surgery on Montesinos knots
Exceptional Dehn surgeries on arborescent knots have been classified except for Seifert fibered surgeries on Montesinos knots of length 3. There are infinitely many of them as it is known that 4n + 6 and 4n + 7 surgeries on a (−2, 3, 2n + 1) pretzel knot are Seifert fibered. It will be shown that there are only finitely many others. A list of 20 surgeries will be given and proved to be Seifert ...
متن کاملOn the quantum sl2 invariants of knots and integral homology spheres
We will announce some results on the values of quantum sl2 invariants of knots and integral homology spheres. Lawrence’s universal sl2 invariant of knots takes values in a fairly small subalgebra of the center of the h-adic version of the quantized enveloping algebra of sl2 . This implies an integrality result on the colored Jones polynomials of a knot. We define an invariant of integral homolo...
متن کاملKnot Invariants in 3-manifolds and Essential Tori
Given a three-manifold M and a cohomology class τ ∈ H(M,Z/nZ), there is a naturally defined invariant of singular knots in M with exactly one double point, Vτ . It has been known that for some manifolds Vτ is integrable and that in these cases it defines an easily computed and highly effective knot invariant. This paper provides necessary and sufficient conditions on M for the integrability of ...
متن کامل