Discrete fundamental groups of Warped Cones and expanders

2017/10/13 by Vigolo, Federico · 3 citations
#51F99 20F34 20F05 57S25 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1710.04955

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.

Cited by

• Coarse cone quotients
• Quasi-isometric embeddings of Ramanujan complexes
• Coarse Baum-Connes and warped cones: failure of surjectivity in odd degree

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