Convergence of group actions in metric measure geometry
Metric Geometry
2021-04-21 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2104.00187,
title = {Convergence of group actions in metric measure geometry},
author = {Hiroki Nakajima and Takashi Shioya},
journal= {arXiv preprint arXiv:2104.00187},
year = {2021}
}
Comments
18 pages