November 8, 2025Open Access

A satellite formula for real Seiberg-Witten Floer homotopy types

Key Points

Main finding reveals the dependence of knot concordance invariants on zero-framed surgery and real Seiberg-Witten theory.
Key evidence demonstrates that a satellite formula for real Seiberg-Witten Floer homotopy types is established for knots.
Approach involves applying a version of the excision theorem to derive results relevant to knot concordance theory.
Significance suggests that this work contributes essential insights into knot theory, particularly in concordance contexts.

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.

A satellite formula for real Seiberg-Witten Floer homotopy types

Key Points

Abstract

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