A Steenrod Square for Link Floer Homology

Fuente: arXiv
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Main Author: Tao, Yan
Format: Preprint
Published: 2025
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author Tao, Yan
author_facet Tao, Yan
contents Recently, Manolescu-Sarkar constructed a stable homotopy type for link Floer homology, which uses grid homology and accounts for all domains that do not pass through a specific square. We explicitly give the framings of the lower-dimensional moduli spaces of the Manolescu-Sarkar construction as well as the more general moduli spaces corresponding to the full grid. Though in the latter case the stable homotopy type is not known, the explicit framings are enough to construct a framed 1-flow category, a construction by Lobb-Orson-Schütz which contains enough information to find the second Steenrod square. Finally, we find an algorithm for computing the second Steenrod square for all versions of grid homology coming from the full grid.
format Preprint
id arxiv_https___arxiv_org_abs_2511_02000
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Steenrod Square for Link Floer Homology
Tao, Yan
Geometric Topology
Algebraic Topology
Recently, Manolescu-Sarkar constructed a stable homotopy type for link Floer homology, which uses grid homology and accounts for all domains that do not pass through a specific square. We explicitly give the framings of the lower-dimensional moduli spaces of the Manolescu-Sarkar construction as well as the more general moduli spaces corresponding to the full grid. Though in the latter case the stable homotopy type is not known, the explicit framings are enough to construct a framed 1-flow category, a construction by Lobb-Orson-Schütz which contains enough information to find the second Steenrod square. Finally, we find an algorithm for computing the second Steenrod square for all versions of grid homology coming from the full grid.
title A Steenrod Square for Link Floer Homology
topic Geometric Topology
Algebraic Topology
url https://arxiv.org/abs/2511.02000