• Corpus ID: 14199274

Hyperbolic three-manifolds with trivial finite type invariants

@article{Murakami1999HyperbolicTW,
  title={Hyperbolic three-manifolds with trivial finite type invariants},
  author={Hitoshi Murakami},
  journal={arXiv: Geometric Topology},
  year={1999}
}
  • H. Murakami
  • Published 1 February 1999
  • Mathematics
  • arXiv: Geometric Topology
We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree. 
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References

SHOWING 1-10 OF 16 REFERENCES
HOMOLOGY SPHERES WITH THE SAME FINITE TYPE INVARIANTS OF BOUNDED ORDERS
For every n ∈ N, we give a direct geometric construction of integral homology spheres that cannot be distinguished by finite type invariants of orders ≤ n. In particular we obtain Z-homology spheres
Ohtsuki's Invariants are of Finite Type
Using a vanishing condition on certain combinations of components of the Jones polynomial for algebraically split links we show that Ohtsuki's invariants of integral homology three spheres are of
On a universal perturbative invariant of 3-manifolds
Using finite type invariants (or Vassiliev invariants) of framed links and the Kirby calculus we construct an invariant of closed oriented three-dimensional manifolds with values in a graded Hopf
On Perturbative PSU(n) Invariants of Rational Homology 3-Spheres
Abstract We construct power series invariants of rational homology 3-spheres from quantum PSU(n) -invariants. The power series can be regarded as perturbative invariants corresponding to the
Three dimensional manifolds, Kleinian groups and hyperbolic geometry
1. A conjectural picture of 3-manifolds. A major thrust of mathematics in the late 19th century, in which Poincare had a large role, was the uniformization theory for Riemann surfaces: that every
An Invariant of Integral Homology 3-Spheres Which Is Universal For All Finite Type Invariants
In [LMO] a 3-manifold invariant $\Omega(M)$ is constructed using a modification of the Kontsevich integral and the Kirby calculus. The invariant $\Omega$ takes values in a graded Hopf algebra of
Quantum field theory and the Jones polynomial
It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones
The perturbative SO(3) invariant of rational homology 3-spheres recovers from the universal perturbative invariant
Abstract For a Lie algebra g and its representation R, the quantum ( g , R) invariant of knots recovers from the Kontsevich invariant through the weight system derived from substitution of g and R
Casson's invariant for oriented homology 3-spheres : an exposition
In the spring of 1985, A. Casson announced an interesting invariant of homology 3-spheres via constructions on representation spaces. This invariant generalizes the Rohlin invariant and gives
Milnor link invariants and quantum 3-manifold invariants
Abstract. Let $ {\cal Z}(M) $ be the 3-manifold invariant of Le, Murakami and Ohtsuki. We show that $ {\cal Z}(M) = 1 + o(n) $, where $ o(n) $ denotes terms of degree $ \geq n $, if M is a
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