A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres

• 成果类型: Article
• 署名作者: Habiro, Kazuo
• 署名单位: Kyoto University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0071-0
• 发表日期: 2008
• 页码: 1-81
• 关键词: finite-type invariants; quantum-invariants; polynomial invariant; ohtsukis invariants; psu(n) invariants; kirby-calculus; 3-manifolds; REPRESENTATIONS; CATEGORIES; ALGEBRAS

摘要

We construct an invariant J(M) of integral homology spheres M with values in a completion (Z[q]) over cap of the polynomial ring Z[ q] such that the evaluation at each root of unity. gives the the SU( 2) Witten-Reshetikhin-Turaev invariant tau(zeta) ( M) of M at. Thus zeta unifies all the SU( 2) Witten Reshetikhin -Turaev invariants of M. It also follows that tau(zeta) (M) as a function on. behaves like an analytic function defined on the set of roots of unity.