On Perturbative PSU(n) Invariants of Rational Homology 3-Spheres

Details On Perturbative PSU(n) Invariants of Rational Homology 3-Spheres On Perturbative PSU(n) Invariants of Rational Homology 3-Spheres

1998-02-06

arxiv.org/abs/math/9802032v2

Mathematics

Geometric Topology

36 Pages. Minor mistakes corrected. Main results slightly improved. Some parts substantially revised

Scientific paper

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 contribution of the trivial connection in the hypothetical Witten's integral. This generalizes a result of Ohtsuki (the $n=2$ case) which led him to the definition of finite type invariants of 3-manifolds. The proof utilizes some symmetry properties of quantum invariants (of links) derived from the theory of affine Lie algebras and the theory of the Kontsevich integral.

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