Abstract:
This paper makes a study of operads and of coalgebras over operads. Certain operads EnEn and EE are defined, constituting the algebraic analogues of the "little nn-cube" operads; it is then shown that the singular chain complex C∗(X;R)C∗(X;R) of a topological space XX is a coalgebra over the operad EE, and that this structure completely determines the weak homotopy type of the space.
Bibliography: 26 titles.
This publication is cited in the following 28 articles:
Imen Rjaiba, “Operad Structures on the Species Composition of Two Operads”, Appl Categor Struct, 33:1 (2025)
Ricardo Campos, Thomas Willwacher, “Operadic torsors”, Journal of Algebra, 458 (2016), 71
S. V. Lapin, “Chain Realization of Differential Modules with $\infty$-Simplicial Faces and the $B$-Construction over $A_\infty$-Algebras”, Math. Notes, 98:1 (2015), 111–129
S. V. Lapin, “Extension of the Multiplication Operation in $E_\infty$-Algebras to an $A_\infty$-Morphism of $E_\infty$-Algebras and Cartan Objects in the Category of May Algebras”, Math. Notes, 89:5 (2011), 672–688
André Hirschowitz, Marco Maggesi, “Modules over monads and initial semantics”, Information and Computation, 208:5 (2010), 545
S. V. Lapin, “Multiplicative $A_\infty$-structure in terms of spectral sequences of fibrations”, J. Math. Sci., 164:1 (2010), 95–118
S. V. Lapin, “$D_\infty$-differential $E_\infty$-algebras and spectral sequences of $D_\infty$-differential modules”, J. Math. Sci., 159:6 (2009), 819–832
S. V. Lapin, “$D_\infty$-differential $E_\infty$-algebras and spectral sequences of fibrations”, Sb. Math., 198:10 (2007), 1379–1406
André Hirschowitz, Marco Maggesi, Lecture Notes in Computer Science, 4576, Logic, Language, Information and Computation, 2007, 218
M.A.. Mandell, “Cochains and homotopy type”, Publ.math.IHES, 103:1 (2006), 213
S. V. Lapin, “$D_\infty$-differential $E_\infty$-algebras and multiplicative spectral sequences”, Sb. Math., 196:11 (2005), 1627–1658
V. A. Smirnov, “Homotopy Theories of Algebras over Operads”, Math. Notes, 78:2 (2005), 251–257
S. V. Lapin, “$(DA)_\infty$-modules over $(DA)_\infty$-algebras and spectral sequences”, Izv. Math., 66:3 (2002), 543–568
V. A. Smirnov, “The $A_\infty$-structures and differentials of the Adams spectral sequence”, Izv. Math., 66:5 (2002), 1057–1086
S. V. Lapin, “$D_\infty$-differential $A_\infty$-algebras
and spectral sequences”, Sb. Math., 193:1 (2002), 119–142
S. N. Tronin, O. A. Kopp, “Matrix linear operads”, Russian Math. (Iz. VUZ), 44:6 (2000), 50–59
V. A. Smirnov, “Homotopy type and $A_\infty$-group structure”, Sb. Math., 189:10 (1998), 1563–1572
V. A. Smirnov, “Lie algebras over operads and their applications in homotopy theory”, Izv. Math., 62:3 (1998), 549–580
Mikhail A. Batanin, “Homotopy coherent category theory and A∞-structures in monoidal categories”, Journal of Pure and Applied Algebra, 123:1-3 (1998), 67
Citation in format AMSBIB
Contact us: