Satellites of infinite rank in the smooth concordance group

• 成果类型: Article
• 署名作者: Hedden, Matthew; Pinzon-Caicedo, Juanita
• 署名单位: Michigan State University; University of Notre Dame
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-01026-w
• 发表日期: 2021
• 页码: 131-157
• 关键词: topologically slice-knots; HOMOLOGY; INVARIANTS; filtration; Operators; LINKS

摘要

We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use SO(3) gauge theory to provide a general criterion sufficient for the image of a satellite operation to generate an infinite rank subgroup of the smooth concordance group C. Our criterion applies widely; notably to many unknotted patterns for which the corresponding operators on the topological concordance group are zero. We raise some questions and conjectures regarding satellite operators and their interaction with concordance.