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arXiv · 1206.1829

The Geometric Invariants of Group Extensions

Nic Koban·Peter Wong
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Abstract

In this paper, we compute the Σ^n(G) and Ω^n(G) invariants when 1 \rightarrow H \rightarrow G \rightarrow K \rightarrow 1 is a short exact sequence of finitely generated groups with K finite. We also give sufficient conditions for G to have the R_{\infty} property in terms of Ω^n(H) and Ω^n(K) when either K is finite or the sequence splits. As an application, we construct a group F \rtimes? Z_2 where F is the R. Thompson's group F and show that F \rtimes Z_2 has the R_{\infty} property while F is not characteristic.

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Nic Koban, Peter Wong. 2012-06-08. The Geometric Invariants of Group Extensions. https://arxiv.org/abs/1206.1829

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