Geodesic
Differential perturbations and $D_\infty$-differential modules
Sbornik. Mathematics, Tome 192 (2001) no. 11, pp. 1639-1659

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In the present paper the notions of a $D_\infty$-differential and a $D_\infty$-differential module are introduced, which are, respectively, homotopically invariant analogues of the differential and the chain complex. Basic homotopic properties of $D_\infty$-differentials and $D_\infty$-differential modules are established. The connection between the Gugenheim–Lambe–Stasheff theory of differential perturbations in homological algebra and the construction of a $D_\infty$-differential module is considered. 
@article{SM_2001_192_11_a2,
     author = {S. V. Lapin},
     title = {Differential perturbations and $D_\infty$-differential modules},
     journal = {Sbornik. Mathematics},
     pages = {1639--1659},
     publisher = {mathdoc},
     volume = {192},
     number = {11},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_11_a2/}
}
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S. V. Lapin. Differential perturbations and $D_\infty$-differential modules. Sbornik. Mathematics, Tome 192 (2001) no. 11, pp. 1639-1659. http://geodesic.mathdoc.fr/item/SM_2001_192_11_a2/