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On the universal cover and the fundamental group of an RCD*(K,N)-space

  • Andrea Mondino EMAIL logo and Guofang Wei

Abstract

The main goal of the paper is to prove the existence of the universal cover for 𝖱𝖢𝖣*(K,N)-spaces. This generalizes earlier work of [43, 44] on the existence of universal covers for Ricci limit spaces. As a result, we also obtain several structure results on the (revised) fundamental group of 𝖱𝖢𝖣*(K,N)-spaces. These are the first topological results for 𝖱𝖢𝖣*(K,N)-spaces without extra structural-topological assumptions (such as semi-local simple connectedness).

Award Identifier / Grant number: DMS-1506393

Award Identifier / Grant number: DMS-1440140

Funding statement: Guofang Wei was partially supported by NSF DMS-1506393.

Acknowledgements

This work was done while both authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California during the Spring 2016 semester, supported by the National Science Foundation under Grant No. DMS-1440140. We thank the organizers of the Differential Geometry Program and MSRI for providing great environment for research and collaboration.

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Received: 2016-06-20
Revised: 2016-09-11
Published Online: 2016-12-21
Published in Print: 2019-08-01

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