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arXiv · 2308.01620

Invariants for Gromov's pyramids and their applications

Syota Esaki·Daisuke Kazukawa·Ayato Mitsuishi
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Abstract

Pyramids introduced by Gromov are generalized objects of metric spaces with Borel probability measures. We study non-trivial pyramids, where non-trivial means that they are not represented as metric measure spaces. In this paper, we establish general theory of invariants of pyramids and construct several invariants. Using them, we distinguish concrete pyramids. Furthermore, we study a space consisting of non-trivial pyramids and prove that the space have infinite dimension.

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Syota Esaki, Daisuke Kazukawa, Ayato Mitsuishi. 2023-08-03. Invariants for Gromov's pyramids and their applications. https://arxiv.org/abs/2308.01620

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