A knot Floer stable homotopy type
Abstract
Given a grid diagram for a knot or link K in , we construct a filtered spectrum whose homology is the knot Floer homology of K. We conjecture that the filtered homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry, but rather builds on the combinatorial definition of grid homology. We inductively define models for the moduli spaces of pseudo-holomorphic strips and disk bubbles, and patch them together into a framed flow category. The inductive step relies on the vanishing of an obstruction class that takes values in a complex of positive domains with partitions.
Keywords
Cite
@article{arxiv.2108.13566,
title = {A knot Floer stable homotopy type},
author = {Ciprian Manolescu and Sucharit Sarkar},
journal= {arXiv preprint arXiv:2108.13566},
year = {2025}
}
Comments
123 pages; changed the marking to be avoided from X to O, so that our construction gives a filtered spectrum; added Theorem 1.1 and its proof (Section 15), changed the models for internal framings (Section 7.3), improved the discussion of signs (Sections 4.2 and 12), added new examples (Section 16); many other smaller changes throughout