SO(3) invariants of Seifert manifolds and their algebraic integrality
Li, Bang-He
arXiv, 0005298 / Harvested from arXiv
For Seifert manifold $M=X({p_1}/_{\f{q_1}},{p_2}/_{\f{q_2}}, ...,{p_n}/_ {\f{q_n}}), \tau^{'}_r(M)$ is calculated for all $r$ odd $\geq 3$. If $r$ is coprime to at least $n-2$ of $p_k$ (e.g. when $M$ is the Poincare homology sphere), it is proved that $(\sqrt {\dfrac{4}{r}}\sin \dfrac{\pi}{r})^{\nu}\tau^{'}_r(M)$ is an algebraic integer in the r-th cyclotomic field, where $\nu$ is the first Betti number of $M$. For the torus bundle obtained from trefoil knot with framing 0, i.e. $X_{tref}(0)=X(-2/_{\f{1}},3/_{\f{1}},6/_{\f{1}}), \tau^{'}_r$ is obtained in a simple form if $3\mid\llap /r$, which shows in some sense that it is impossible to generalize Ohtsuki's invariant to 3-manifolds being not rational homology spheres.
Publié le : 2000-05-31
Classification:  Mathematics - Quantum Algebra,  Mathematical Physics,  Mathematics - Geometric Topology
@article{0005298,
     author = {Li, Bang-He},
     title = {SO(3) invariants of Seifert manifolds and their algebraic integrality},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0005298}
}
Li, Bang-He. SO(3) invariants of Seifert manifolds and their algebraic integrality. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0005298/