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Mathematische Annalen

, Volume 373, Issue 1–2, pp 355–396 | Cite as

Discrete fundamental groups of warped cones and expanders

  • Federico VigoloEmail author
Article
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Abstract

In this paper we compute the discrete fundamental groups of warped cones. As an immediate consequence, this allows us to show that there exist coarsely simply-connected expanders and superexpanders. This also provides a strong coarse invariant of warped cones and implies that many warped cones cannot be coarsely equivalent to any box space.

Mathematics Subject Classification

Primary: MSC 51F99 MSC 20F34 20F05 57S25 Secondary: 05C99 20F65 54E35 

Notes

Acknowledgements

I wish to thank my advisor Cornelia Druţu for her continuous support and encouragement and David Hume, Richard Wade and Gareth Wilkes for helpful discussions and for pointing out the example in Remark 53. I should also thank Wouter van Limbeek for drawing my attention to Example 69.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of OxfordOxfordUnited Kingdom

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