Transferring algebra structures up to homology equivalence

Leif Johansson, Larry Lambe

Abstract


Given a strong deformation retract $M$ of an algebra $A$, there are several apparently distinct ways ([9],[19],[13],[24],[15],[18],[17]) of constructing a coderivation on the tensor coalgebra of $M$ in such a way that the resulting complex is quasi isomorphic to the classical (differential tor) [17] bar construction of $A$. We show that these methods are equivalent and are determined combinatorially by an inductive formula first given in a very special setting in [16]. Applications to de Rham theory and Massey products are given.

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DOI: http://dx.doi.org/10.7146/math.scand.a-14337

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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