Homotopy lifting property of an $e^ε$-Lipschitz and co-Lipschitz map

Shicheng Xu

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arXiv · 1211.5919

Homotopy lifting property of an $e^ε$-Lipschitz and co-Lipschitz map

Shicheng Xu

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Abstract

An $e^ε$-Lipschitz and co-Lipschitz map, as a metric analogue of an $ε$-Riemannian submersion, naturally arises from a sequence of Alexandrov spaces with curvature uniformly bounded below that converges to a space of only weak singularities. In this paper we prove its homotopy lifting property and its homotopy stability in Gromov-Hausdorff topology. Due to an overlook in the previous version, the part for bounding intrinsic distance of fibers will be talked about in the coming papers.

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Shicheng Xu. 2013-01-13. Homotopy lifting property of an $e^ε$-Lipschitz and co-Lipschitz map. https://arxiv.org/abs/1211.5919

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