Homology groups of types in stable theories and the Hurewicz correspondence [article]

John Goodrick, Byunghan Kim, Alexei Kolesnikov
2016 arXiv   pre-print
We give an explicit description of the homomorphism group H_n(p) of a strong type p in any stable theory under the assumption that for every non-forking extension q of p the groups H_i(q) are trivial for i at least 2 but less than n. The group H_n(p) turns out to be isomorphic to the automorphism group of a certain piece of the algebraic closure of n independent realizations of p; it was shown earlier by the authors that such a group must be abelian. We call this the "Hurewicz correspondence"
more » ... analogy with the Hurewicz Theorem in algebraic topology.
arXiv:1412.3864v2 fatcat:xx6axk5xordu3e4zyr2c5zo2gm