Counting flat cycles in the homology of locally symmetric spaces

2022/06/23 by Studenmund, Daniel, Tshishiku, Bena
#11F75 #57R19 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2206.11986

Abstract

Locally symmetric spaces like SL(n,\mathbb Z)\backslash SL_n(\mathbb R)/SO(n) contain immersed compact flat manifolds of dimension equal to the real rank. We give a lower bound for the contribution of these cycles to the homology of congruence covers. Similar results are proved for other families of locally symmetric spaces.

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