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.
Keywords:
differential module with homotopy simplicial faces, A∞-algebra, D∞-differential module, realization of a simplicial topological space, SDR-data, category of F∞-modules, category of D∞-modules.
Citation:
S. V. Lapin, “Homotopy Simplicial Faces and the Homology of Realizations of Simplicial Topological Spaces”, Mat. Zametki, 94:5 (2013), 661–681; Math. Notes, 94:5 (2013), 619–635
This publication is cited in the following 7 articles:
S. V. Lapin, “Dihedral modules with ∞-simplicial faces and dihedral homology of involutive A∞-algebras over rings”, St. Petersburg Math. J., 33:3 (2022), 491–509
Lapin V S., “Homotopy Invariance of the Cyclic Homology of a(Infinity)-Algebras Under Homotopy Equivalences of a(Infinity)-Algebras”, Georgian Math. J., 28:6 (2021), 895–916
S. V. Lapin, “Homotopy invariance of dihedral homology of involutive A∞-algebras”, St. Petersburg Math. J., 33:6 (2022), 949–969
Lapin V S., “Dihedral Infinity-Simplicial Modules and Dihedral Homology of Involutive Homotopy Unital a(Infinity)-Algebras”, Georgian Math. J., 26:2 (2019), 257–286
S. V. Lapin, “Cyclic homology of cyclic infinity-simplicial modules”, Georgian Math. J., 25:4 (2018), 571–591
S. V. Lapin, “Cyclic Modules with ∞-Simplicial Faces and the Cyclic Homology of A∞-Algebras”, Math. Notes, 102:6 (2017), 806–823
S. V. Lapin, “Chain Realization of Differential Modules with ∞-Simplicial Faces and the B-Construction over A∞-Algebras”, Math. Notes, 98:1 (2015), 111–129
Citation in format AMSBIB
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