A satellite formula for real Seiberg-Witten Floer homotopy types

2025/04/04 by Jin Miyazawa, Miyazawa, Jin, JungHwan Park +3 · 2 citations
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.2504.03270

openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a satellite formula for the real Seiberg-Witten Floer homotopy types of knots with odd patterns. Using this, we derive several applications to knot concordance theory. The satellite formula follows from a version of the excision theorem for real Floer homotopy types. Additionally, we show that the concordance invariants arising from real Seiberg-Witten theory depend only on the knot's zero-framed surgery.

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