Degree of -Alexander torsion for 3-manifolds

• 成果类型: Article
• 署名作者: Liu, Yi
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0680-6
• 发表日期: 2017
• 页码: 981-1030
• 关键词: thurston norm; Lower bounds; INVARIANTS

摘要

For an irreducible orientable compact 3-manifold N with empty or incompressible toral boundary, the full -Alexander torsion associated to any real first cohomology class of N is represented by a function of a positive real variable t. The paper shows that is continuous, everywhere positive, and asymptotically monomial in both ends. Moreover, the degree of equals the Thurston norm of . The result confirms a conjecture of J. Dubois, S. Friedl, and W. Luck and addresses a question of W. Li and W. Zhang. Associated to any admissible homomorphism , the -Alexander torsion is shown to be continuous and everywhere positive provided that G is residually finite and is weakly acyclic. In this case, a generalized degree can be assigned to . Moreover, the generalized degree is bounded by the Thurston norm of phi.