Article
Algebra Structures on the Comparison of the Reduced Bar Construction and the Reduced W-Construction
Author/s | Álvarez Solano, Víctor
![]() ![]() ![]() ![]() ![]() ![]() ![]() Armario Sampalo, José Andrés ![]() ![]() ![]() ![]() ![]() ![]() ![]() Frau García, María Dolores ![]() ![]() ![]() ![]() ![]() ![]() ![]() Real Jurado, Pedro ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2009 |
Deposit Date | 2021-06-25 |
Published in |
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Abstract | For a simplicial augmented algebra K, Eilenberg–Mac Lane constructed a chain map . They proved that g is a reduction (homology isomorphism) and conjectured that it is also the injection of a contraction (special homotopy ... For a simplicial augmented algebra K, Eilenberg–Mac Lane constructed a chain map . They proved that g is a reduction (homology isomorphism) and conjectured that it is also the injection of a contraction (special homotopy equivalence). The contraction is followed at once by using homological perturbation techniques. If K is commutative, Eilenberg–Mac Lane proved that g is a morphism of DGA-algebras. The present article is devoted to proving that f and φ satisfy certain multiplicative properties (weaker than g) and showing how they can be used for computing in an economical way the homology of twisted cartesian products of two Eilenberg–Mac Lane spaces. |
Funding agencies | Junta de Andalucía |
Project ID. | FQM–296
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Citation | Álvarez Solano, V., Armario Sampalo, J.A., Frau García, M.D. y Real Jurado, P. (2009). Algebra Structures on the Comparison of the Reduced Bar Construction and the Reduced W-Construction. Communications in Algebra, 37 (10), 3643-3665. |
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