# Discrete fundamental groups of warped cones and expanders

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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

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**(preprint)**

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