Abstract:
In the present paper the construction of a D∞-differential
A∞-(co)algebra is introduced and basic homotopy properties of this construction are studied. The connection between D∞-differential A∞-(co)algebras and
spectral sequences is established, which enables us to construct the structure of
an A∞ -coalgebra on the Milnor coalgebra directly from the differentials of the Adams spectral sequence.
This publication is cited in the following 13 articles:
Joana Cirici, Anna Sopena-Gilboy, “Filtered 𝐴-infinity structures in complex geometry”, Proc. Amer. Math. Soc., 150:9 (2022), 4067
Lapin V S., “Homotopy Invariance of the Cyclic Homology of a(Infinity)-Algebras Under Homotopy Equivalences of a(Infinity)-Algebras”, Georgian Math. J., 28:6 (2021), 895–916
Lapin V S., “Dihedral Infinity-Simplicial Modules and Dihedral Homology of Involutive Homotopy Unital a(Infinity)-Algebras”, Georgian Math. J., 26:2 (2019), 257–286
Joana Cirici, Daniela Egas Santander, Muriel Livernet, Sarah Whitehouse, “Derived A-infinity algebras and their homotopies”, Topology and its Applications, 235 (2018), 214
Herscovich E., “Spectral Sequences Associated to Deformations”, J. Homotopy Relat. Struct., 12:3 (2017), 513–548
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
Lapin S.V., “Homotopy Properties of Differential Modules With Simplicial F-Infinity-Faces and D-Infinity-Differential Modules”, Georgian Math. J., 22:4 (2015), 543–562
S. V. Lapin, “
D
∞-differential E
∞-algebras and Steenrod operations in spectral sequences”, Journal of Mathematical Sciences (New York), 152:3 (2008), 372
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
S. V. Lapin, “$D_\infty$-differential $E_\infty$-algebras and multiplicative spectral sequences”, Sb. Math., 196:11 (2005), 1627–1658
S. V. Lapin, “$(DA)_\infty$-modules over $(DA)_\infty$-algebras and spectral sequences”, Izv. Math., 66:3 (2002), 543–568
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