Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 33 min ago
PreprintCC BYHAL

Depth of free-by-cyclic groups

  • Spencer Dowdall
  • Yassine Guerch
  • Radhika Gupta
  • Jean Pierre Mutanguha
  • Caglar Uyanik
Open at sourcePDFDOICite

Abstract

For a free group automorphism, we prove that its poset of attracting lamination orbits is a canonical invariant of the associated mapping torus. That is, if a free-by-cyclic group splits as a mapping torus in two different ways, then the corresponding automorphisms have isomorphic posets of lamination orbits. Further, we show that the lamination depth, the size of the largest chain in this poset, is a commensurability invariant of the free-by-cyclic group.

Related

  1. Finite index rigidity of free-by-cyclic groups
    Radhika Gupta, Nir Lazarovich
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. The Diophantine Problem with constraints in some free-by-cyclic groups
    Laura Ciobanu, Robert D. Gray, Alex Levine
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Finiteness properties of centralisers in Out(FN) and automorphisms of free-by-cyclic groups
    Naomi Andrew, Yassine Guerch, Camille Horbez +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  4. Conjugator Length in Iterated Cyclic Amalgams of Free Groups
    Conan Gillis
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Fuglede's Conjecture for Cyclic Groups of Square-free Order
    Hu Tan, Ying Zhang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{dowdall2026depth,
  title = {{Depth of free-by-cyclic groups}},
  author = {Spencer Dowdall and Yassine Guerch and Radhika Gupta and Jean Pierre Mutanguha and Caglar Uyanik},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2602.10433},
  eprint = {2602.10433},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05798895v1},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - Depth of free-by-cyclic groups
AU  - Spencer Dowdall
AU  - Yassine Guerch
AU  - Radhika Gupta
AU  - Jean Pierre Mutanguha
AU  - Caglar Uyanik
PY  - 2026
DA  - 2026/10/14
PB  - HAL
DO  - 10.48550/arxiv.2602.10433
UR  - https://hal.science/hal-05798895v1
AB  - For a free group automorphism, we prove that its poset of attracting lamination orbits is a canonical invariant of the associated mapping torus. That is, if a free-by-cyclic group splits as a mapping torus in two different ways, then the corresponding automorphisms have isomorphic posets of lamination orbits. Further, we show that the lamination depth, the size of the largest chain in this poset, is a commensurability invariant of the free-by-cyclic group.
ER  -