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arXiv · 1503.04564

A classification of 2-chains having 1-shell boundaries in rosy theories

Byunghan Kim·SunYoung Kim·Junguk Lee
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Abstract

We classify, in a non-trivial amenable collection of functors, all 2-chains up to the relation of having the same 1-shell boundary. In particular, we prove that in a rosy theory, every 1-shell of a Lascar strong type is the boundary of some 2-chain, hence making the 1st homology group trivial. We also show that, unlike in simple theories, in rosy theories there is no upper bound on the minimal lengths of $2$-chains whose boundary is a $1$-shell.

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Byunghan Kim, SunYoung Kim, Junguk Lee. 2015-03-16. A classification of 2-chains having 1-shell boundaries in rosy theories. https://arxiv.org/abs/1503.04564

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