Core surfaces

Magee, Michael; Puder, Doron

Abstract

Let Γg be the fundamental group of a closed connected orientable surface of genus g≥2. We introduce a combinatorial structure of core surfaces, that represent subgroups of Γg. These structures are (usually) 2-dimensional complexes, made up of vertices, labeled oriented edges, and 4g-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.

Citation

Magee, M., & Puder, D. (2022). Core surfaces. Geometriae Dedicata, 216(4), Article 46. https://doi.org/10.1007/s10711-022-00706-6

• Journal Article Type: Article
• Acceptance Date: May 25, 2022
• Online Publication Date: Jun 16, 2022
• Publication Date: 2022-08
• Deposit Date: Jul 27, 2022
• Publicly Available Date: Jun 16, 2023
• Journal: Geometriae Dedicata
• Print ISSN: 0046-5755
• Electronic ISSN: 1572-9168
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 216
• Issue: 4
• Article Number: 46
• DOI: https://doi.org/10.1007/s10711-022-00706-6
• Public URL: https://durham-repository.worktribe.com/output/1196691