{
  "abstract": "We build a Floer theory on the space of braids of periodic orbits of a Hamiltonian flow on a closed symplectic surface. The differential and continuation maps are defined by counting Floer isotopies of braids: tuples of Floer cylinders with pairwise disjoint graphs. With this new perspective, we prove a quantitative braid stability result that shows the persistence of braids under possibly large Hamiltonian perturbations. As an application, we show that for every $α\\geq 0$ there is a sequence of Hamiltonian diffeomorphisms $ϕ_k$ on the two-torus $T^2$ such that $$d_H(\\operatorname{Ent}_{\\leq α}(T^2,ω),ϕ_k)\\to \\infty \\quad (k \\to \\infty),$$ where $\\text{Ent}_{\\leq α}(T^2,ω)\\subset \\text{Ham}(T^2,ω)$ denotes the set of Hamiltonian diffeomorphisms with topological entropy at most $α$ and $d_H$ the Hofer metric. We prove this result by studying only contractible periodic orbits, whereas analogous higher-genus statements were previously obtained using non-contractible orbits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34961",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicolas Grunder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7pwty8k3tna8s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34961",
  "fulltext_url": null,
  "id": "7pwty8k3tna8s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34961",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214744008",
  "pdf_url": "https://arxiv.org/pdf/2609.34961",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7pwty8k3tna8s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.34961",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34961"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Braid Stability and a Floer theory of Braid Isotopies",
  "title_text": "Braid Stability and a Floer theory of Braid Isotopies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/7pwty8k3tna8s",
  "venue": "arXiv",
  "versions": []
}