Volume 10, issue 1 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Bar constructions and Quillen homology of modules over operads

John E Harper

Algebraic & Geometric Topology 10 (2010) 87–136
1 M Basterra, André–Quillen cohomology of commutative $S$–algebras, J. Pure Appl. Algebra 144 (1999) 111 MR1732625
2 M Basterra, M A Mandell, Homology and cohomology of $E_{\infty}$ ring spectra, Math. Z. 249 (2005) 903 MR2126222
3 C Berger, I Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003) 805 MR2016697
4 W Chachólski, J Scherer, Homotopy theory of diagrams, Mem. Amer. Math. Soc. 155 (2002) MR1879153
5 D Dugger, D C Isaksen, Topological hypercovers and $\mathbb{A}^1$–realizations, Math. Z. 246 (2004) 667 MR2045835
6 W G Dwyer, H W Henn, Homotopy theoretic methods in group cohomology, Advanced Courses in Mathematics. CRM Barcelona, Birkhäuser Verlag (2001) MR1926776
7 W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology", North-Holland (1995) 73 MR1361887
8 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Mathematical Surveys and Monographs 47, American Mathematical Society (1997) MR1417719
9 A D Elmendorf, M A Mandell, Rings, modules, and algebras in infinite loop space theory, Adv. Math. 205 (2006) 163 MR2254311
10 B Fresse, Lie theory of formal groups over an operad, J. Algebra 202 (1998) 455 MR1617616
11 B Fresse, Koszul duality of operads and homology of partition posets, from: "Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic $K$–theory", Contemp. Math. 346, Amer. Math. Soc. (2004) 115 MR2066499
12 B Fresse, Modules over operads and functors, Lecture Notes in Mathematics 1967, Springer (2009) MR2494775
13 P Gabriel, M Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 35, Springer New York, New York (1967) MR0210125
14 P G Goerss, On the André–Quillen cohomology of commutative $\mathbb{F}_2$–algebras, Astérisque (1990) 169 MR1089001
15 P G Goerss, M J Hopkins, André–Quillen (co)-homology for simplicial algebras over simplicial operads, from: "Une dégustation topologique [Topological morsels]: homotopy theory in the Swiss Alps (Arolla, 1999)", Contemp. Math. 265, Amer. Math. Soc. (2000) 41 MR1803952
16 P G Goerss, M J Hopkins, Moduli spaces of commutative ring spectra, from: "Structured ring spectra", London Math. Soc. Lecture Note Ser. 315, Cambridge Univ. Press (2004) 151 MR2125040
17 P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Mathematics 174, Birkhäuser Verlag (1999) MR1711612
18 P Goerss, K Schemmerhorn, Model categories and simplicial methods, from: "Interactions between homotopy theory and algebra", Contemp. Math. 436, Amer. Math. Soc. (2007) 3 MR2355769
19 V K A M Gugenheim, J P May, On the theory and applications of differential torsion products, Memoirs of the American Mathematical Society 142, American Mathematical Society (1974) MR0394720
20 J E Harper, Homotopy theory of modules over operads in symmetric spectra, Algebr. Geom. Topol. 9 (2009) 1637 MR2539191
21 J E Harper, Homotopy theory of modules over operads and non–$\Sigma$ operads in monoidal model categories, J. Pure Appl. Algebra (to appear) arXiv:0801.0191
22 V Hinich, Homological algebra of homotopy algebras, Comm. Algebra 25 (1997) 3291 MR1465117
23 P S Hirschhorn, Model categories and their localizations, Mathematical Surveys and Monographs 99, American Mathematical Society (2003) MR1944041
24 M Hovey, Model categories, Mathematical Surveys and Monographs 63, American Mathematical Society (1999) MR1650134
25 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
26 M Kapranov, Y Manin, Modules and Morita theorem for operads, Amer. J. Math. 123 (2001) 811 MR1854112
27 I Kříž, J P May, Operads, algebras, modules and motives, Astérisque 233 (1995) MR1361938
28 S Mac Lane, Homology, Classics in Mathematics, Springer (1995) MR1344215
29 S Mac Lane, Categories for the working mathematician, Graduate Texts in Mathematics 5, Springer (1998) MR1712872
30 M A Mandell, $E_\infty$ algebras and $p$–adic homotopy theory, Topology 40 (2001) 43 MR1791268
31 M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. $(3)$ 82 (2001) 441 MR1806878
32 J P May, The geometry of iterated loop spaces, Lectures Notes in Mathematics 271, Springer (1972) MR0420610
33 J P May, Classifying spaces and fibrations, Mem. Amer. Math. Soc. 1 (1975) MR0370579
34 J P May, Simplicial objects in algebraic topology, Chicago Lectures in Mathematics, University of Chicago Press (1992) MR1206474
35 J E McClure, J H Smith, A solution of Deligne's Hochschild cohomology conjecture, from: "Recent progress in homotopy theory (Baltimore, MD, 2000)", Contemp. Math. 293, Amer. Math. Soc. (2002) 153 MR1890736
36 H Miller, Correction to: “The Sullivan conjecture on maps from classifying spaces” [Ann. of Math. (2) 120 (1984) 39–87], Ann. of Math. $(2)$ 121 (1985) 605 MR794376
37 D G Quillen, Homotopical algebra, Lecture Notes in Mathematics 43, Springer (1967) MR0223432
38 D Quillen, Rational homotopy theory, Ann. of Math. $(2)$ 90 (1969) 205 MR0258031
39 D Quillen, On the (co-) homology of commutative rings, from: "Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol XVII, New York, 1968)", Amer. Math. Soc. (1970) 65 MR0257068
40 C Rezk, Spaces of Algebra Structures and Cohomology of Operads, PhD thesis, MIT (1996)
41 C Rezk, Notes on the Hopkins–Miller theorem, from: "Homotopy theory via algebraic geometry and group representations (Evanston, IL, 1997)", Contemp. Math. 220, Amer. Math. Soc. (1998) 313 MR1642902
42 S Schwede, Spectra in model categories and applications to the algebraic cotangent complex, J. Pure Appl. Algebra 120 (1997) 77 MR1466099
43 S Schwede, $S$–modules and symmetric spectra, Math. Ann. 319 (2001) 517 MR1819881
44 S Schwede, Stable homotopy of algebraic theories, Topology 40 (2001) 1 MR1791267
45 S Schwede, An untitled book project about symmetric spectra (2007)
46 S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. $(3)$ 80 (2000) 491 MR1734325
47 B Shipley, A convenient model category for commutative ring spectra, from: "Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic $K$–theory", Contemp. Math. 346, Amer. Math. Soc. (2004) 473 MR2066511
48 M Spitzweck, Operads, algebras and modules in general model categories (2001) arXiv:0101102
49 C A Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press (1994) MR1269324