Core Surfaces
Group Theory
2022-06-22 v2 Geometric Topology
Abstract
Let be the fundamental group of a closed connected orientable surface of genus . We introduce a combinatorial structure of "core surfaces", that represent subgroups of . These structures are (usually) 2-dimensional complexes, made up of vertices, labeled oriented edges, and -gons. They are compact whenever the corresponding subgroup is finitely generated. The theory of core surfaces that we initiate here is analogous to the influential and fruitful theory of Stallings core graphs for subgroups of free groups.
Cite
@article{arxiv.2108.00717,
title = {Core Surfaces},
author = {Michael Magee and Doron Puder},
journal= {arXiv preprint arXiv:2108.00717},
year = {2022}
}
Comments
23 pages, 7 figures. Minor improvements in presentation following referee's comments. arXiv admin note: text overlap with arXiv:2003.05892