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

2015/03/16 by Byunghan Kim, Kim, Byunghan, SunYoung Kim +3
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topology and Set Theory #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1503.04564

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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