Non-reduction of relations in the Gromov space to Polish actions

Jesús A. Álvarez López; Alberto Candel

doi:10.1215/00294527-2017-0026

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arXiv · 1501.02606

Non-reduction of relations in the Gromov space to Polish actions

Jesús A. Álvarez López·Alberto Candel

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Abstract

It is shown that, in the Gromov space of isometry classes of pointed proper metric spaces, the equivalence relations defined by existence of coarse quasi-isometries or being at finite Gromov-Hausdorff distance, cannot be reduced to the equivalence relation defined by any Polish action.

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BibTeX RIS

Jesús A. Álvarez López, Alberto Candel. 2017-10-28. Non-reduction of relations in the Gromov space to Polish actions. https://doi.org/10.1215/00294527-2017-0026

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