A unified quantum SO(3) invariant for rational homology 3-spheres

• 成果类型: Article
• 署名作者: Beliakova, Anna; Buehler, Irmgard; Le, Thang
• 署名单位: University of Zurich; University System of Georgia; Georgia Institute of Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0304-5
• 发表日期: 2011
• 页码: 121-174
• 关键词: 3-manifold invariants; reshetikhin-turaev; integrality; witten; sums

摘要

Given a rational homology 3-sphere M with |H (1)(M,acurrency sign)|=b and a link L inside M, colored by odd numbers, we construct a unified invariant I (M,L) belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten-Reshetikhin-Turaev invariants of the pair (M,L). If b=1 and L=a..., I (M) coincides with Habiro's invariant of integral homology 3-spheres. For b > 1, the unified invariant defined by the third author is determined by I (M) . Important applications are the new Ohtsuki series (perturbative expansions of I (M) ) dominating quantum SO(3) invariants at roots of unity whose order is not a power of a prime. These series are not known to be determined by the LMO invariant.