Free-group presentation conjecture for finitely presented path triangulations

A finitely presented path triangulation free group is a free group associated with a finitely presented path triangulation. A free group presentation is a presentation of a group by free generators and relations, and a triangulated digital image is a digital image equipped with a triangulation. Free-group presentation conjecture. Every finitely presented path triangulation free group occurs as a free group presentation of some triangulated digital image. This conjecture is framed as a transition from path triangulations to digital topology, in the setting of results asserting that finitely presented groups can occur as digital fundamental groups; the supplied text does not provide a resolution.

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Primary source

James F. Peters, “Path Triangulation, Cycles and Good Covers on Planar Cell Complexes. Extension of J.H.C. Whitehead's Homotopy System Geometric Realization and E.C. Zeeman's Collapsible Cone Theorems”, arXiv:2208.12760 (2022).

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