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A spectral sequence for the homology of a finite algebraic delooping

  • Birgit Richter (a1) and Stephanie Ziegenhagen (a2)

In the world of chain complexes En-algebras are the analogues of based n-fold loop spaces in the category of topological spaces. Fresse showed that operadic En-homology of an En-algebra computes the homology of an n-fold algebraic delooping. The aim of this paper is to construct two spectral sequences for calculating these homology groups and to treat some concrete classes of examples such as Hochschild cochains, graded polynomial algebras and chains on iterated loop spaces. In characteristic zero we gain an identification of the summands in Pirashvili's Hodge decomposition of higher order Hochschild homology in terms of derived functors of indecomposables of Gerstenhaber algebras and as the homology of exterior and symmetric powers of derived Kähler differentials.

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An71. Donald W. Anderson , Chain functors and homology theories, Symposium on Algebraic Topology (Battelle Seattle Res. Center, Seattle, Wash., 1971), Lecture Notes in Math. 249, Springer, Berlin, (1971), 112.

DKS93. William G. Dwyer , Daniel M. Kan , Christopher R. Stover , An E2-model category structure for pointed simplicial spaces, Journal of Pure and Applied Algebra 90 (1993), 137152.

F11a. Benoit Fresse , Iterated bar complexes of E-infinity algebras and homology theories, Alg. Geom. Topol. 11 (2011), 747838.

F11b. Benoit Fresse , Koszul duality of En-operads, Selecta Math. (N.S.) 17(2) (2011), 363434.

GM07. Gerald Gaudens , Luc Menichi , Batalin-Vilkovisky algebras and the J-homomorphism, Topology Appl. 156(2) (2008), 365374.

Ge63. Murray Gerstenhaber , The cohomology structure of an associative ring, Ann. of Math. 78(2) (1963), 267288.

Gi08. Grégory Ginot , Higher order Hochschild cohomology, C. R. Math. Acad. Sci. Paris 346(1-2) (2008), 510.

LR11. Muriel Livernet , Birgit Richter , An interpretation of En-homology as functor homology, Mathematische Zeitschrift 269(1) 2011, 193219.

Ma66. J. Peter May , The cohomology of restricted Lie algebras and of Hopf algebras, J. Algebra 3 (1966), 123146.

MS02. James McClure , Jeffrey Smith , A solution of Deligne's Hochschild cohomology conjecture, Recent progress in homotopy theory (Baltimore, MD, 2000), Con-temp. Math. 293, Amer. Math. Soc., Providence, RI (2002), 153193.

Mi78. Haynes Miller , A spectral sequence for the homology of an infinite delooping, Pacific J. Math. 79(1) (1978), 139155.

MM65. John W. Milnor , John C. Moore , On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211264.

Ri01. Birgit Richter , Taylor towers of Gamma-modules, Annales de l'Institut Fourier 51(4) (2001), 9951023.

RS65. Melvin G. Rothenberg , Norman E. Steenrod , The cohomology of classifying spaces of H-spaces, Bull. Amer. Math. Soc. 71 (1965), 872875.

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Journal of K-Theory
  • ISSN: 1865-2433
  • EISSN: 1865-5394
  • URL: /core/journals/journal-of-k-theory
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