Convergence of group actions in metric measure geometry

Hiroki Nakajima; Takashi Shioya

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arXiv · 2104.00187

Convergence of group actions in metric measure geometry

Hiroki Nakajima·Takashi Shioya

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Abstract

We generalize the box and observable distances to those between metric measure spaces with group actions, and prove some fundamental properties. As an application, we obtain an example of a sequence of lens spaces with unbounded dimension converging to the cone of the infinite-dimensional complex projective space. Our idea is to use the theory of mass-transport.

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Hiroki Nakajima, Takashi Shioya. 2021-04-20. Convergence of group actions in metric measure geometry. https://arxiv.org/abs/2104.00187

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