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PreprintCC BY 4.0arXiv

Limiting laminations and boundary weights for infinite-type mapping classes

  • Carolyn Abbott
  • Phuong Pham
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Abstract

For every infinite-type surface with an isolated puncture that admits a shift map and every natural number n, we study an intrinsically infinite-type mapping class gn and a simple closed curve whose orbit under gn splits into n subsequences, each of which converges in the coarse Chabauty topology to a geodesic lamination on the surface. These laminations are cyclically permuted by gn, and their union is a gn--invariant geodesic lamination. We further show the attracting limit point of gn in the boundary of the relative arc graph has weight n. In particular, intrinsically infinite-type loxodromic isometries of the relative arc graph realize every finite weight.

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Cite

BibTeXRIS
BibTeX
@misc{abbott2026limiting,
  title = {{Limiting laminations and boundary weights for infinite-type mapping classes}},
  author = {Carolyn Abbott and Phuong Pham},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25435},
  eprint = {2609.25435},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25435},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Limiting laminations and boundary weights for infinite-type mapping classes
AU  - Carolyn Abbott
AU  - Phuong Pham
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25435
UR  - https://arxiv.org/abs/2609.25435
AB  - For every infinite-type surface with an isolated puncture that admits a shift map and every natural number n, we study an intrinsically infinite-type mapping class g_n and a simple closed curve whose orbit under g_n splits into n subsequences, each of which converges in the coarse Chabauty topology to a geodesic lamination on the surface. These laminations are cyclically permuted by g_n, and their union is a g_n--invariant geodesic lamination. We further show the attracting limit point of g_n in the boundary of the relative arc graph has weight n. In particular, intrinsically infinite-type loxodromic isometries of the relative arc graph realize every finite weight.
ER  -