Homology groups of types in stable theories and the Hurewicz correspondence

John Goodrick, Byunghan Kim, Alexei Kolesnikov
2017 Annals of Pure and Applied Logic  
We give an explicit description of the homology 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 2 ≤ i < n. The group H n (p) turns out to be isomorphic to the automorphism group of a certain part of the algebraic closure of n independent realizations of p; it follows from the authors' earlier work that such a group must be abelian. We call this the "Hurewicz correspondence" by analogy with
more » ... he Hurewicz Theorem in algebraic topology. els. North Holland, 1990.
doi:10.1016/j.apal.2017.03.007 fatcat:pipqtxckhfdfxkykvjjqe4lcr4