Mod p and torsion homology growth in nonpositive curvature

• 成果类型: Article
• 署名作者: Avramidi, Grigori; Okun, Boris; Schreve, Kevin
• 署名单位: Max Planck Society; University of Wisconsin System; University of Wisconsin Milwaukee; University of Chicago
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01057-x
• 发表日期: 2021
• 页码: 711-723
• 关键词: approximating l-2-invariants

摘要

We compute the mod p homology growth of residual sequences of finite index normal subgroups of right-angled Artin groups. We find examples where this differs from the rational homology growth, which implies the homology of subgroups in the sequence has lots of torsion. More precisely, the homology torsion grows exponentially in the index of the subgroup. For odd primes p, we construct closed locally CAT(0) manifolds with nonzero mod p homology growth outside the middle dimension. These examples show that Singer's conjecture on rational homology growth and Luck's conjecture on torsion homology growth are incompatible with each other, so at least one of them must be wrong.