Additive posets, CW-complexes, and graphs
Vladimir Turaev
TL;DR
This paper introduces additive posets and explores their properties, demonstrating that the top homology group of finite CW-complexes forms an additive poset invariant under subdivisions, with applications to CW-complexes and graphs.
Contribution
The paper defines additive posets and proves that the top homology group of finite CW-complexes has an additive poset structure invariant under subdivisions.
Findings
Top homology groups of finite CW-complexes form additive posets
Additive posets are invariant under subdivisions
Applications to graphs and CW-complexes are discussed
Abstract
We introduce and study additive posets. We show that the top homology group (with coefficients in Z/2Z) of a finite dimensional CW-complex carries a structure of an additive poset invariant under subdivisions. Applications to CW-complexes and graphs are discussed.
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