We give an explicit description of the homology group Hn(p) of a strong type p in any stable theory under the assumption that for every non-forking extension q of p the groups Hi(q) are trivial for 2≤i<n. The group Hn(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 the Hurewicz Theorem in algebraic topology.
Bibliographical noteFunding Information:
The second author was supported by NRF of Korea grant 2013R1A1A2073702, and Samsung Science Technology Foundation under Project Number SSTF-BA1301-03.
All Science Journal Classification (ASJC) codes