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arXiv · 1006.2237

Persistent homology of groups

Graham Ellis·Simon A. King
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Abstract

We introduce and investigate notions of persistent homology for p-groups and for coclass trees of p-groups. Using computer techniques we show that persistent homology provides fairly strong homological invariants for p-groups of order at most 81. The strength of these invariants, and some elementary theoretical properties, suggest that persistent homology may be a useful tool in the study of prime-power groups.

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Graham Ellis, Simon A. King. 2010-06-11. Persistent homology of groups. https://arxiv.org/abs/1006.2237

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