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PreprintCC BY 4.0arXiv

Khovanov monodromy groups via motions

  • Gabriel Corrigan
  • Livio Ferretti
  • Isacco Nonino
  • Susanna Terron
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Abstract

For any link, we define a monodromy map from the motion group of the link to the group of automorphisms of the link's Khovanov homology. The image of this map is the \emph{unoriented monodromy group} of the link. This map allows us to convert results concerning motion groups of links into ones about their Khovanov monodromy. In particular, we use a characterisation of the motion groups of split links to write their unoriented monodromy groups as an explicit semidirect product in terms of their unsplit pieces. We give some demonstrative examples, computing the unoriented monodromy groups of unlinks, Hopf links, and split links composed of pieces thereof.

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Cite

BibTeXRIS
BibTeX
@misc{corrigan2026khovanov,
  title = {{Khovanov monodromy groups via motions}},
  author = {Gabriel Corrigan and Livio Ferretti and Isacco Nonino and Susanna Terron},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03932},
  eprint = {2609.03932},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03932},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Khovanov monodromy groups via motions
AU  - Gabriel Corrigan
AU  - Livio Ferretti
AU  - Isacco Nonino
AU  - Susanna Terron
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03932
UR  - https://arxiv.org/abs/2609.03932
AB  - For any link, we define a monodromy map from the motion group of the link to the group of automorphisms of the link's Khovanov homology. The image of this map is the \emph{unoriented monodromy group} of the link. This map allows us to convert results concerning motion groups of links into ones about their Khovanov monodromy. In particular, we use a characterisation of the motion groups of split links to write their unoriented monodromy groups as an explicit semidirect product in terms of their unsplit pieces. We give some demonstrative examples, computing the unoriented monodromy groups of unlinks, Hopf links, and split links composed of pieces thereof.
ER  -