2000/05/31 by Banghe Li, Bang-He Li, Li, Bang-He
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.GT #math.MP #math.QA
paper · pdf · doi:10.48550/arxiv.math/0005298
Latex
arxiv created 2000/05/31 · openalex publication_date 2000/05/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For Seifert manifold M=X(p1/_\fq1,p2/_\fq2, ...,pn/_ \fqn), τ'r(M) is calculated for all r odd ≥ 3. If r is coprime to at least n-2 of pk (e.g. when M is the Poincare homology sphere), it is proved that (√ \dfrac4rsin \dfracπr)ντ'r(M) is an algebraic integer in the r-th cyclotomic field, where ν is the first Betti number of M. For the torus bundle obtained from trefoil knot with framing 0, i.e. Xtref(0)=X(-2/_\f1,3/_\f1,6/_\f1), τ'r is obtained in a simple form if 3|\llap /r, which shows in some sense that it is impossible to generalize Ohtsuki's invariant to 3-manifolds being not rational homology spheres.