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Geometric realisation over aspherical groups
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abstract
We prove that the direct sums of extensions of scalars of relation modules are geometrically realisable as the second homotopy group of a finite 2-complex. We use this to exhibit a finite 2-complex with fundamental group the $(10,15)$ torus knot group and non-free $\pi_2$, yielding exotic presentations of a group for which no such examples had previously been known. We conclude by constructing stably free non-free modules over an infinite family of Baumslag-Solitar groups; it remains to determine whether these modules are geometrically realisable by finite 2-complexes.
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Cited by 1 Pith paper
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LlamaRec-LKG-RAG: A Single-Pass, Learnable Knowledge Graph-RAG Framework for LLM-Based Ranking
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