Filtered Instantons and the Concordance of Satellites

2025/07/18 by Ivan So, So, Ivan
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2507.14350

openalex publication_date 2025/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In \citeNST23, Nozaki-Sato-Taniguchi defined a family of invariants r_s for integer homology spheres with filtered instanton homology \citeFS92. Coupling these with techniques in classical knot theory, we produce some results in the knot concordance group, including criteria for a family of satellite knots to be linearly independent and the independence of what we call the Whitehead n -ble P_n .

Citations

• Filtered instanton homology and cosmetic surgery
• Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology
• Instantons, special cycles, and knot concordance
• Instantons, concordance, and Whitehead doubling
• Equivariant aspects of Yang-Mills Floer theory
• On the homology cobordism group of homology 3-spheres

Related

• Knot concordance, the point class in instanton homology and Donaldson invariants
• Instantons, Bar-Natan homology, and some concordance invariants of knots
• Instantons, special cycles, and knot concordance
• Instantons, concordance, and Whitehead doubling
• Framed instanton homology and concordance, II