Cosimplicial objects and little n-cubes I

American Journal of Mathematics

Volumn 126, Issue 5, 2004, Pages 1109-1153

  McClure, James E ^a   Smith, Jeffrey H ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 5744235105     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. J. F. Adams, Infinite Loop Spaces, Ann. of Math. Stud., vol. 90, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1978.
2. M. Batanin, Coherent categories with respect to monads and coherent prohomotopy theory, Cahiers Topologie Géom. Différentielle Catég. 34 (1993), 279-304.
3. ∞-structures in monoidal categories, J. Pure Appl. Algebra 123 (1998), 67-103.
4. n-spaces, preprint available at http://front.math.ucdavis.edu/math.CT/0207281.
5. n-operads, Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995), Contemp. Math., vol. 202, Amer. Math. Soc., Providence, RI, 1997, pp. 37-52.
6. J. M. Boardman and R. M. Vogt, Homotopy-everything H-spaces, Bull. Amer. Math. Soc. 74 (1968), 1117-1122.
7. A. K. Bousfield and D. M. Kan, Homotopy Limits, Completions and Localizations, Lectures Notes in Math., vol. 304, Springer-Verlag, Berlin-New York, 1972.
8. P. Deligne, Letter to Stasheff et al., May 17, 1993.
9. M. Gerstenhaber and A. Voronov, Homotopy G-algebras and moduli space operad, Internat. Math. Res. Notices 1995:3 (1995), 141-153.
10. E. Getzler, Batalin-Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys. 159 (1994), 265-285.
11. D. R. Grayson, Exterior power operations on higher K-theory, K-Theory 3 (1989), 247-260.
12. V. A. Hinich and V. V. Schechtman, On homotopy limit of homotopy algebras. K-theory, Arithmetic and Geometry (Moscow, 1984-1986), Lecture Notes in Math., vol. 1289, Springer-Verlag, Berlin, 1987, pp. 240-264.
13. P. S. Hirschhorn, Model Categories and Their Localizations, Math. Surveys Monogr., vol. 99, American Mathematical Society, Providence, RI, 2003.
14. M. Kontsevich, Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1999), 35-72.
15. M. Kontsevich and Y. Soibelman, Deformations of algebras over operads and the Deligne conjecture, Conférence Moshé Flato 1999, Volume I, Math. Phys. Stud., vol. 22, Kluwer Acad. Publ., Dordrecht, 2000, pp. 255-307.
16. I. Kriz and J. P. May, Operads, algebras, modules and motives, Asterisque 233 (1995).
17. S. Mac Lane, Categories for the Working Mathematician, 2nd ed., Springer-Verlag, Berlin-New York, 1998.
18. M. Markl, S. Shnider, and J. Stasheff, Operads in Algebra, Topology and Physics, Math. Surveys Monogr., vol. 96, American Mathematical Society, Providence, RI, 2002.
19. J. P. May, The Geometry of Iterated Loop Spaces, Lectures Notes in Math., vol. 271, Springer-Verlag, Berlin-New York, 1972.
20. J. E. McClure and J. H. Smith, A solution of Deligne's Hochschild cohomology conjecture, Recent Progress in Homotopy Theory (Baltimore, MD, 2000), Contemp. Math., vol. 293, Amer. Math. Soc., Providence, RI, 2002, pp. 153-193.
21. -, Operads and cosimplicial objects: an introduction, Axiomatic, Enriched and Motivic Homotopy Theory: Proceedings of a NATO Advanced Study Institute at the Isaac Newton Institute for Mathematical Sciences, Kluwer Acad. Publ., Dordrecht, 2004, pp. 133-171.
22. -, Cosimplicial objects and little n-cubes. II, in preparation.
23. nX, Israel J. Math. 66 (1989), 330-350.
24. D. Tamarkin, Another proof of M. Kontsevich formality theorem, preprint, available at http://front.math.ucdavis.edu/math.QA/9803025.
25. -, Formality of chain operad of small squares, preprint, available at http://front.math.ucdavis.edu/math.QA/9809164.
26. R. W. Thomason, Uniqueness of delooping machines, Duke Math. J. 46 (1979), 217-252.