On denominators of the Kontsevich integral and the universal perturbative invariant of 3-manifolds

• 成果类型: Article
• 署名作者: Le, TTQ
• 署名单位: State University of New York (SUNY) System; University at Buffalo, SUNY
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050298
• 发表日期: 1999
• 页码: 689-722
• 关键词: vassiliev

摘要

The integrality of the Kontsevich integral and perturbative invariants is discussed. It is shown that the denominator of the degree n part of the Kontsevich integral of any knot or link is a divisor of (2!3!... n!)(4)(n + 1)!. We prove this by establishing the existence of a Drinfeld's associator in the space of chord diagrams with special denominators. We also show that the denominator of the degree n part of the universal perturbative invariant of homology 3-spheres is not divisible by any prime greater than 2n + 1.