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Deformation retracts and the Hochschild homology of polynomial rings. (English) Zbl 0844.18008

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 \(C^\infty (S^1; A)\)”.

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
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References:

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[2] Loday, J.-L., Cyclic Homology (1992), Berlin: Springer-Verlag, Berlin · Zbl 0780.18009
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