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arXiv · 2508.01041

Nonlocal loss of first homotopy in polyhedral approximations of Peano continua

Jeremy Brazas·Hanspeter Fischer
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Abstract

If a Peano continuum $X$ is semilocally simply connected, then it has a finite polyhedral approximation whose fundamental group is isomorphic to that of $X$. In general, this fails to be true. It is known that the fundamental group of a locally complicated Peano continuum may contain nontrivial elements that are persistently undetectable by polyhedral approximations, at all scales. However, we show that such failure is not inherently local.

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Jeremy Brazas, Hanspeter Fischer. 2025-08-01. Nonlocal loss of first homotopy in polyhedral approximations of Peano continua. https://doi.org/10.1016/j.topol.2025.109710

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