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Limits of manifolds in the Gromov-Hausdorff metric spaceHegenbarth, Friedrich, 1940- ; Repovš, Dušan, 1954-We apply the Gromov-Hausdorff metric ▫$d_G$▫ for characterization of certain generalized manifolds. Previously, we have proven that with respect to the metric ▫$d_G$▫, generalized ▫$n$▫-manifolds are ... limits of spaces which are obtained by gluing two topological ▫$n$▫-manifolds by a controlled homotopy equivalence (the so-called 2-patch spaces). In the present paper, we consider the so-called manifold-like generalized ▫$n$▫-manifolds ▫$X^{n}$▫, introduced in 1966 by Mardeić and Segal, which are characterized by the existence of ▫$\delta$▫-mappings ▫$f_{\delta }$▫ of ▫$X^{n}$▫ onto closed manifolds ▫$M^{n}_{\delta }$▫, for arbitrary small ▫$\delta >0$▫, i.e., there exist onto maps ▫$f_{\delta }:X^{n}\rightarrow M^{n}_{\delta}$▫ such that for every ▫$M^{n}_{\delta }$▫, ▫$f^{-1}_{\delta }(u)$▫ has diameter less than ▫$\delta$▫. We prove that with respect to the metric ▫$d_G$▫, manifold-like generalized ▫$n$▫-manifolds ▫$X^{n}$▫ are limits of topological ▫$n$▫-manifolds ▫$M^{n}_{i}$▫. Moreover, if topological ▫$n$▫-manifolds ▫$M^{n}_{i}$▫ satisfy a certain local contractibility condition ▫${\mathcal {M}}(\varrho, n)$▫, we prove that generalized ▫$n$▫-manifold ▫$X^{n}$▫ is resolvable.Vir: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 20, iss. 1, Feb. 2023, art: 47 (11 str.))Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasleLeto - 2023Jezik - angleškiCOBISS.SI-ID - 135986179
Avtor
Hegenbarth, Friedrich, 1940- |
Repovš, Dušan, 1954-
Teme
Gromov-Hausdorff metric |
Gromov topological moduli space |
manifold-like generalized manifold |
absolute neighborhood |
retract |
cell-like map |
▫$\delta$▫-map |
structure map |
controlled surgery sequence |
▫$\varepsilon$▫-homotopy |
2-patch space
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Avtor | Hegenbarth, Friedrich, 1940- ; Repovš, Dušan, 1954- |
Naslov | Limits of manifolds in the Gromov-Hausdorff metric space |
Datum objave | 2022-12-28 |
COBISS.SI-ID | 135986179 |
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Topologija in njena uporaba | P1-0292-2022 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
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Algebrajski odtisi geometrijskih značilnosti v homologiji | N1-0114-2019 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
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vir: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 20, iss. 1, Feb. 2023, art: 47 (11 str.))
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Povezave do osebnih bibliografij avtorjev | Povezave do podatkov o raziskovalcih v sistemu SICRIS |
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Hegenbarth, Friedrich, 1940- | 28253 |
Repovš, Dušan, 1954- | 07083 |
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