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arXiv · 2607.13736

Filling 1-cycles, 2-cycle complexity, and torsion growth

Cameron Gates Rudd
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Abstract

For 2-complexes with trivial first Betti number, we study quantitative connections between filling inequalities for 1-cycles, the complexity of the second homology, and the size of the torsion part of the first homology. For 2-complexes whose fundamental groups have property $(\tau)$ with respect to all finite index normal subgroups, we prove a geometric lower bound on the logarithm of the size of the first homology of finite covers.

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Cameron Gates Rudd. 2026-07-15. Filling 1-cycles, 2-cycle complexity, and torsion growth. https://arxiv.org/abs/2607.13736

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