Perturbation theory in differential homological algebra. I
The main object of this paper is the comparison of several theorems in homological algebra. The theorems are found in [1] [\textit{V. K. A. M. Gugenheim} and \textit{H. J. Munkholm}, J. Pure Appl. Algebra 4, 9-29 (1974; Zbl 0358.18015)], [2] [\textit{V. K. A. M. Gugenheim} and \textit{J. Stasheff}, Bull. Soc. Math. Belg., Ser. A 38, 237-246 (1986; Zbl 0639.55008)] and [3] [\textit{V. K. A. M. Gugenheim} and \textit{J. P. May}, Mem. Am. Math. Soc. 142 (1974; Zbl 0292.55019)]. In particular, [1] is shown to be a special case of [2]. It is furthermore shown how special cases of the ``distinguished resolution'' of [3] can be constructed using the algorithms for ``twisting cochains'' discussed in this paper and hence they give an alternate method for constructing the free resolutions over the group ring of certain two-stage nilpotent groups given earlier by the second author [Bull. Soc. Math. Belg., Ser. A 38, 247-264 (1986; Zbl 0632.55010) and Computers in geometry and topology, Proc. Conf., Chicago/Ill. 1986, Lect. Notes Pure Appl. Math. 114, 189-209 (1989)].
free resolutions over the group ring of two-stage nilpotent groups
scientific article; zbMATH DE number 4080417