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Peer-reviewedCC BYGroups, Geometry, and Dynamics

Connectedness of a space of branched coverings with a periodic cycle

  • Laurent Bartholdi
Open at sourcePDFDOICite

Abstract

We prove the connectedness of the following locus: the space of degree- d branched self-coverings of S^{2} with two critical points of order d , one of which is n -periodic. Equivalently, all branched self-coverings of S^{2} with two critical points of order d , one of which is n -periodic, are combinatorially equivalent.

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Cite

BibTeXRIS
BibTeX
@article{bartholdi2026connectedness,
  title = {{Connectedness of a space of branched coverings with a periodic cycle}},
  author = {Laurent Bartholdi},
  journal = {Groups, Geometry, and Dynamics},
  year = {2026},
  month = nov,
  doi = {10.4171/ggd/781},
  eprint = {2204.11130},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05849734v1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Connectedness of a space of branched coverings with a periodic cycle
AU  - Laurent Bartholdi
PY  - 2026
DA  - 2026/11/03
JO  - Groups, Geometry, and Dynamics
DO  - 10.4171/ggd/781
UR  - https://hal.science/hal-05849734v1
AB  - We prove the connectedness of the following locus: the space of degree- d branched self-coverings of S^{2} with two critical points of order d , one of which is n -periodic. Equivalently, all branched self-coverings of S^{2} with two critical points of order d , one of which is n -periodic, are combinatorially equivalent.
SN  - 1661-7207
SN  - 1661-7215
ER  -