Elements of Homology Theory

By V. Prasolov. 2007

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Convex equipartitions: the spicy chicken theorem (2013, background): “led discussion, see [7, p. 51].” It refers to page 51 of the paper [6] for a “more detailed” discussion. In the paper [6] the same claim is repeated, and the reader is referred to page 48 of the book [33] to justify the fact that (co)homology with compact support is not a homotopy invariant, a fact ”
Cohomology of digraphs and (undirected) graphs (2015, background): “For the definition and basic properties of homology and cohomology groups of a simplicial complex we refer to [17] and [23].”
Graphs associated with simplicial complexes (2014, background): “Introduction In a recent paper [9], the authors developed the theory of homology of path complexes, which can be considered as a natural generalization of a simplicial homology theory (see, for example, [10], [11], and [12]).”