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A partially ordered set (poset) is a set along with an associated partial order. Homology is a method from algebraic topology of assigning a sequence of abelian groups to a topological space. It is standard to define the homology of a poset as the homology of the order complex of the poset. We introduce a new notion of mod 2 homology of a certain type of poset and explore the properties of this version of poset homology. We also attempt to discover when our mod 2 homology agrees with the usual homology on posets.
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Barnett, Ian Michael, "Mod 2 Homology of Posets" (2013). Senior Projects Spring 2013. 83.