Quantum Topology· 2026Q1
A filtered mapping cone formula for cables of the knot meridian
- 1citations
- Q1SCImago
- 2026year
Short summary
A new filtered mapping cone formula is developed to compute the knot Floer complex of (n,1)-cables of knot meridians in rational surgeries.
AI-generated from the title and abstract; the full text is not read.
Key points
- A novel filtered mapping cone formula is constructed for (n,1)-cable knot meridians in rational surgeries.
- The formula generalizes existing results for large surgery and filtered mapping cones.
- It proves the existence of knots in integer homology spheres with arbitrary u_{i,j} concordance homomorphism values.
- The formula facilitates the creation of knots bounding PL surfaces with arbitrarily large genus in homology balls.
AI-generated from the title and abstract; the full text is not read.
Abstract
We construct a filtered mapping cone formula that computes the knot Floer complex of the (n,1) -cable of the knot meridian in any rational surgery, generalizing Truong’s result about the (n,1) -cable of the knot meridian in large surgery and Hedden–Levine’s filtered mapping cone formula. As an application, we show that there exist knots in integer homology spheres with arbitrary \varphi_{i,j} values for any i>j\geq 0 , where \varphi_{i,j} are the concordance homomorphisms defined in the work of Dai–Hom–Stoffregen–Truong. This formula also leads to the construction of knots in integer homology spheres that bound PL surfaces with arbitrarily large genus in a homology ball in the work of Hom–Stoffregen–Zhou.
The authors' abstract, as published at the source. Quantum Topology, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Geometry and Topology
Geometry and TopologyMathematics