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arXiv · 1909.01309

The full spectrum of scl on recursively presented groups

Nicolaus Heuer
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Abstract

We show that the set $SCL^{rp}$ of stable commutator lengths on recursively presented groups equals the set of non-negative right-computable numbers. Hence all non-negative algebraic or computable numbers are in $SCL^{rp}$ and $SCL^{rp}$ is not closed under subtraction. We also show that every non-negative real number is the stable commutator length of an element in some infinitely presented small cancellation group.

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Nicolaus Heuer. 2019-09-03. The full spectrum of scl on recursively presented groups. https://arxiv.org/abs/1909.01309

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