Lattices, graphs, and Conway mutation

• 成果类型: Article
• 署名作者: Greene, Joshua Evan
• 署名单位: Boston College
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0421-4
• 发表日期: 2013
• 页码: 717-750
• 关键词: homology; THEOREM; LINKS; knot

摘要

The d-invariant of an integral, positive definite lattice I > records the minimal norm of a characteristic covector in each equivalence class . We prove that the 2-isomorphism type of a connected graph is determined by the d-invariant of its lattice of integral flows (or cuts). As an application, we prove that a reduced, alternating link diagram is determined up to mutation by the Heegaard Floer homology of the link's branched double-cover. Thus, alternating links with homeomorphic branched double-covers are mutants.