Lindenstrauss, Ayelet Deformation retracts and the Hochschild homology of polynomial rings. (English) Zbl 0844.18008 Isr. J. Math. 93, 317-332 (1996). Author’s abstract: “We assume given a ring \(A\) with unit, and a subcomplex of the reduced bar complex of \(A\). We assume that this subcomplex is a deformation retract of the whole complex and thus has homology equal to the Hochschild homology of \(A\), but it will typically be smaller and easier to calculate with. We use these to construct (accordingly small) deformation retracts for the reduced bar complexes of \(A[t]\) and \(A[t, t^{- 1}]\). When \(A\) is a Banach algebra, we also do this construction for \(C^\infty (S^1; A)\)”. Reviewer: R.Fröberg (Stockholm) MSC: 18G60 Other (co)homology theories (MSC2010) 16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) 18G55 Nonabelian homotopical algebra (MSC2010) 46H99 Topological algebras, normed rings and algebras, Banach algebras 55U15 Chain complexes in algebraic topology 57T30 Bar and cobar constructions Keywords:reduced bar complex; Hochschild homology; deformation retracts; Banach algebra PDFBibTeX XMLCite \textit{A. Lindenstrauss}, Isr. J. Math. 93, 317--332 (1996; Zbl 0844.18008) Full Text: DOI References: [1] Kassel, C., Homologie cyclique, caractère de Chern, et lemme de perturbation, Journal für die Reine und Angewandte Mathematik, 408, 159-180 (1990) · Zbl 0691.18002 · doi:10.1515/crll.1990.408.159 [2] Loday, J.-L., Cyclic Homology (1992), Berlin: Springer-Verlag, Berlin · Zbl 0780.18009 [3] Wolffhardt, K., The Hochschild homology of complete intersections, Transactions of the American Mathematical Society, 171, 51-66 (1972) · Zbl 0269.14018 · doi:10.2307/1996374 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.