Finding simple curves in surface covers is undecidable

DOI10.1007/s10711-019-00482-wzbMath1467.57014arXiv1806.03700OpenAlexW2974054363MaRDI QIDQ2181579

Ingrid Irmer

Publication date: 19 May 2020

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.03700

zbMATH Keywords

3-manifoldssimple loop conjecturesimple curves on surfacescovers of surface groups

Mathematics Subject Classification ID

Covering spaces and low-dimensional topology (57M10) Topological methods in group theory (57M07) Fundamental group, presentations, free differential calculus (57M05) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Cites Work

• Unnamed Item
• The simple loop conjecture for 3-manifolds modeled on Sol
• On the self-intersections of curves deep in the lower central series of a surface group
• Recursive unsolvability of group theoretic problems
• Algorithms for Jordan curves on compact surfaces
• \(\pi_1\)-injective surfaces in graph manifolds
• Lifts of simple curves in finite regular coverings of closed surfaces
• Minimal Surfaces in Manifolds with S 1 Actions and the Simple Loop Conjecture for Seifert Fibered Spaces
• An Algorithm for Simple Curves on Surfaces
• Algorithmen für einfache Kurven auf Flächen.
• Simple Closed Curves on Surraces
• Embedding Theorems for Groups

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