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A natural (and efficient) way to approximate an isomanifold is to consider its piecewise-linear (PL) approximation based on a triangulation <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal {T}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>T<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of the ambient space <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbb {R}}^d$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>R<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mi>d<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. In this paper, we give conditions under which the PL approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine and thick triangulation <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal {T}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>T<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fr\u00e9chet distance between the original isomanifold and its PL approximation. Finally, we show analogous results for the PL approximation of an isomanifold with boundary.<\/jats:p>","DOI":"10.1007\/s10208-021-09520-0","type":"journal-article","created":{"date-parts":[[2021,7,13]],"date-time":"2021-07-13T18:12:34Z","timestamp":1626199954000},"page":"967-1012","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Topological Correctness of PL Approximations of Isomanifolds"],"prefix":"10.1007","volume":"22","author":[{"given":"Jean-Daniel","family":"Boissonnat","sequence":"first","affiliation":[]},{"given":"Mathijs","family":"Wintraecken","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,13]]},"reference":[{"issue":"5","key":"9520_CR1","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1016\/j.cag.2006.07.021","volume":"30","author":"Timothy S Newman","year":"2006","unstructured":"Timothy\u00a0S. Newman and Hong Yi. 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