2005/12/19 by Thang T. Q. Lê, Thang T. Q. Le, Le, Thang T. Q.
Mathematics · #57M25 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0512433
19 pages. Minor typos corrected
openalex publication_date 2005/12/19 · arxiv created 2006/01/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the quantum SO(3)-invariant of an arbitrary 3-manifold M is always an algebraic integer, if the order of the quantum parameter is co-prime with the order of the torsion part of H1(M,\BZ). An even stronger integrality, known as cyclotomic integrality, was established by Habiro for integral homology 3-spheres. Here we generalize Habiro's result to all rational homology 3-spheres.