Additive posets, CW-complexes, and graphs

We introduce additive posets and study their properties and invariants. We show that the top homology group of a finite dimensional CW-complex carries a natural structure of an additive poset invariant under subdivisions of the CW-complex. Applications to graphs are discussed.
The talk is based on my preprint [1]. The author is partially supported by the Laboratory of Quantum Topology of Chelyabinsk State University (Russian Federation government grant 14.Z50.31.0020).
References:

• V. Turaev, Additive posets, CW-complexes, and graphs. arXiv:1605.07798.