Configuration homological ${\mathbb Z}_2$-invariants of manifolds

The paper describes the construction of configuration invariants of 3-manifolds. These invariants are based on defining 3-manifolds by their special spines and can be constructed in the following way. Let $P$ be a special polyhedron and $k\in\mathbb{N}$. To each ordered sequence $\xi$, consisting of $k$ elements of the second homology group of the polyhedron $P$ with coefficients in $\mathbb{Z}_2 $, using a configuration map $\omega$ we assign the number $\omega(P, \xi)\in \{0, 1\}$. The value of the invariant is the ratio of the number of sequences $\xi$ for which $\omega(P, \xi) = 1$ to the total number of all such sequences. The axioms that the configuration map must satisfy ensure the invariance of the resulting rational number under $T$-transformations of special polyhedra.