Skip to content
DraconiticResearch
Search Sources API
186,631 studies31 sourcesUpdated 15 min ago
PreprintCC BY-NC-SA 4.0arXiv

Exact triangle and spectral sequence of the equivariant Floer homology of double branched covers

  • Jinzhou Huang
Open at sourcePDFDOICite

Abstract

In [OS05] the authors proved an exact triangle for the Heegaard Floer homology of the double branched covers associated to a skein sequence of links, and constructed a spectral sequence from the reduced Khovanov homology to the Heegaard Floer homology of the double branched cover of a link. For L ⊂ S3 a link and Σ(L) its double branched cover, the invariant HF(Σ(L)) doesn't capture the information of the natural involution on Σ(L). In this paper we study the equivariant version of HF(Σ(L)) and prove that similar exact triangle and spectral sequence hold for this equivariant version.

Related

  1. An Equivariant Main Conjecture for Branched ℤp-Towers of Finite Graphs and Applications
    Rusiru Gambheera
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  2. Equivariant Instanton Homology
    Mike Miller Eismeier
    Memoirs of the American Mathematical SocietyPeer-reviewedLicence not statedFull text6 citedGeometry & topologyOpenAlex
  3. Equivariant Grid Homology for Strongly Invertible Knots
    Giovanni Framba
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. Spectral Numbers in Tate Rabinowitz Floer Homology
    Kai Cieliebak, Urs Frauenfelder
    arXivPreprintCC BY 4.0Full textGeometry & topologyMathematical physicsarXiv
  5. Spectral Numbers in Tate Rabinowitz Floer Homology
    Kai Cieliebak, Urs Frauenfelder
    Symmetry, Integrability and Geometry: Methods and ApplicationsPeer-reviewedCC BY-SA 4.0Full textGeometry & topologyCrossref

Cite

BibTeXRIS
BibTeX
@misc{huang2026exact,
  title = {{Exact triangle and spectral sequence of the equivariant Floer homology of double branched covers}},
  author = {Jinzhou Huang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38117},
  eprint = {2609.38117},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38117},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Exact triangle and spectral sequence of the equivariant Floer homology of double branched covers
AU  - Jinzhou Huang
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38117
UR  - https://arxiv.org/abs/2609.38117
AB  - In [OS05] the authors proved an exact triangle for the Heegaard Floer homology of the double branched covers associated to a skein sequence of links, and constructed a spectral sequence from the reduced Khovanov homology to the Heegaard Floer homology of the double branched cover of a link. For L ⊂ S^3 a link and Σ(L) its double branched cover, the invariant HF(Σ(L)) doesn't capture the information of the natural involution on Σ(L). In this paper we study the equivariant version of HF(Σ(L)) and prove that similar exact triangle and spectral sequence hold for this equivariant version.
ER  -