Postnikov extensions of ring spectra
Algebraic and Geometric Topology, Tome 6 (2006) no. 4, pp. 1785-1829
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We give a functorial construction of k–invariants for ring spectra and use these to classify extensions in the Postnikov tower of a ring spectrum.

DOI : 10.2140/agt.2006.6.1785
Keywords: ring spectrum, k-invariant, Postnikov extension

Dugger, Daniel  1   ; Shipley, Brooke  2

1 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
2 Department of Mathematics, University of Illinois at Chicago, Chicago, IL 60607, USA
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Dugger, Daniel; Shipley, Brooke. Postnikov extensions of ring spectra. Algebraic and Geometric Topology, Tome 6 (2006) no. 4, pp. 1785-1829. doi: 10.2140/agt.2006.6.1785

[1] M Basterra, André-Quillen cohomology of commutative $S$-algebras, J. Pure Appl. Algebra 144 (1999) 111

[2] M Basterra, M A Mandell, Homology and cohomology of $E_\infty$ ring spectra, Math. Z. 249 (2005) 903

[3] H J Baues, Combinatorial foundation of homology and homotopy, Springer Monographs in Mathematics, Springer (1999)

[4] D Blanc, W G Dwyer, P G Goerss, The realization space of a $\Pi$-algebra: a moduli problem in algebraic topology, Topology 43 (2004) 857

[5] D Dugger, Classification spaces of maps in model categories

[6] D Dugger, Combinatorial model categories have presentations, Adv. Math. 164 (2001) 177

[7] D Dugger, B Shipley, Topological equivalences for differential graded algebras

[8] W G Dwyer, D M Kan, Calculating simplicial localizations, J. Pure Appl. Algebra 18 (1980) 17

[9] W G Dwyer, D M Kan, Function complexes in homotopical algebra, Topology 19 (1980) 427

[10] W G Dwyer, D M Kan, A classification theorem for diagrams of simplicial sets, Topology 23 (1984) 139

[11] P Goerss, M Hopkins, Moduli problems for structured ring spectra, preprint (2005)

[12] M Hovey, Model categories, Mathematical Surveys and Monographs 63, American Mathematical Society (1999)

[13] M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149

[14] A Lazarev, Homotopy theory of $A_\infty$ ring spectra and applications to $M\mathrm{U}$-modules, $K$-Theory 24 (2001) 243

[15] M Mandell, private communication

[16] M A Mandell, B Shipley, A telescope comparison lemma for THH, Topology Appl. 117 (2002) 161

[17] D Quillen, Higher algebraic $K$-theory. I, from: "Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972)", Springer (1973)

[18] S Schwede, B Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. $(3)$ 80 (2000) 491

[19] B Shipley, $H\mathbb{Z}$-algebra spectra are differential graded algebras, to appear Amer. J. Math.

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