Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion

• Autorzy: Anna Beliakova , Christian Blanchet , Thang T. Q. Lê
• Języki publikacji: EN

Abstrakty

EN

For every rational homology 3-sphere with H₁(M,ℤ) = (ℤ/2ℤ)ⁿ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root, and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of quantum SU(2) invariants. New results on the Ohtsuki series and the integrality of quantum invariants are the main applications of our construction.

Kategorie tematyczne

• 57M25: Knots and links in S 3
• 57N10: Topology of general 3 -manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 201
• Numer: 3
• Strony: 217-239

Daty

wydano

2008

Twórcy

autor

Anna Beliakova

• Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

autor

Christian Blanchet

• Institut de Mathématiques de Jussieu, (UMR-CNRS 7586), Université Paris Diderot, 175 rue du Chevaleret, F-75013 Paris, France

autor

Thang T. Q. Lê

• School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, U.S.A.

Identyfikatory

DOI

10.4064/fm201-3-2