{
  "abstract": "Let M be a plumbed integral homology sphere 3-manifold associated with a connected negative definite plumbing graph $Γ$. One of its most important invariants is its multivariable Poincaré series (or zeta function) $f_Γ(\\mathbf {t})$. Several numerical invariants can be read from $f_Γ(\\mathbf{t})$, or even from its `polynomial part' $ \\operatorname{Pol}_Γ(\\mathbf{t})$. For example, the `normalized' Casson's invariant equals $ \\operatorname{Pol}_Γ(1)$. In this note we provide several splice (surgery) formulae for $f_Γ$ and $\\operatorname{Pol}_Γ$ (reduced to the node variables, or to the node variables of connected sub-graphs). In this way, these global invariants can be recovered from a collection of certain smaller graphs. Recall that some (integral homology sphere) 3-manifold invariants are additive with respect to the splice decomposition (like the Casson's invariant). However, some invariants need some `splice correction terms'. In our formulae the correction terms are easily computable one variable Alexander polynomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16840",
  "author_total": 3,
  "authors": [
    {
      "name": "Tamás László"
    },
    {
      "name": "András Némethi"
    },
    {
      "name": "György Tőtős"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ehcxm1qttjnpr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16840",
  "fulltext_url": null,
  "id": "ehcxm1qttjnpr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16840",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7213406600",
  "pdf_url": "https://arxiv.org/pdf/2609.16840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ehcxm1qttjnpr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Splice formulae for Poincaré series of integral homology spheres",
  "title_text": "Splice formulae for Poincaré series of integral homology spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/ehcxm1qttjnpr",
  "venue": "arXiv",
  "versions": []
}