Satellites of Infinite Rank in the Smooth Concordance Group
| Autor: | Matthew Hedden, Juanita Pinzón-Caicedo |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Conjecture
Rank (linear algebra) Group (mathematics) General Mathematics Concordance Image (category theory) 010102 general mathematics Winding number Geometric topology Zero (complex analysis) Geometric Topology (math.GT) 01 natural sciences Mathematics::Geometric Topology Combinatorics Mathematics - Geometric Topology 0103 physical sciences Physics::Space Physics FOS: Mathematics 57M25 57N70 57M27 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Inventiones Mathematicae |
| DOI: | 10.48550/arxiv.1809.04186 |
| Popis: | 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 $\mathcal{C}$. 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. Comment: Significant changes and improvements to exposition. Numerous minor corrections and updates |
| Databáze: | OpenAIRE |
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