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Homotopy simplicial faces and the homology of realizations of simplicial topological spaces

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Abstract

The notion of a differential module with homotopy simplicial faces is introduced, which is a homotopy analog of the notion of a differential module with simplicial faces. The homotopy invariance of the structure of a differential module with homotopy simplicial faces is proved. Relationships between the construction of a differential module with homotopy simplicial faces and the theories of A ∞-algebras and D ∞-differential modules are found. Applications of the method of homotopy simplicial faces to describing the homology of realizations of simplicial topological spaces are presented.

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  1. Saransk, Russia

    S. V. Lapin

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  1. S. V. Lapin
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Correspondence to S. V. Lapin.

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Original Russian Text © S. V. Lapin, 2013, published in Matematicheskie Zametki, 2013, Vol. 94, No. 5, pp. 661–681.

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Lapin, S.V. Homotopy simplicial faces and the homology of realizations of simplicial topological spaces. Math Notes 94, 619–635 (2013). https://doi.org/10.1134/S0001434613110035

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