Cohomology operations and the Deligne conjecture

Martin Markl

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 473-503
  • ISSN: 0011-4642

Abstract

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The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.

How to cite

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Markl, Martin. "Cohomology operations and the Deligne conjecture." Czechoslovak Mathematical Journal 57.1 (2007): 473-503. <http://eudml.org/doc/31143>.

@article{Markl2007,
abstract = {The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.},
author = {Markl, Martin},
journal = {Czechoslovak Mathematical Journal},
keywords = {cohomology; natural operation; cohomology; natural operation},
language = {eng},
number = {1},
pages = {473-503},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Cohomology operations and the Deligne conjecture},
url = {http://eudml.org/doc/31143},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Markl, Martin
TI - Cohomology operations and the Deligne conjecture
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 473
EP - 503
AB - The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.
LA - eng
KW - cohomology; natural operation; cohomology; natural operation
UR - http://eudml.org/doc/31143
ER -

References

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  1. Combinatorial models for real configuration spaces and E n -operads, In: Operads: Proceedings of Renaissance Conferences. Contemporary Math., Vol. 202, J. L.  Loday, J. D.  Stasheff, and A. A.  Voronov (eds.), Am. Math. Soc., 1997, pp. 37–52. (1997) MR1436916
  2. Pre-Lie algebras and the rooted trees operad, Internat. Math. Res. Not. 8 (2001), 395–408. (2001) MR1827084
  3. 10.1090/S0894-0347-02-00399-5, J.  Am. Math. Soc. 15 (2002), 787–815. (2002) MR1915819DOI10.1090/S0894-0347-02-00399-5
  4. 10.1016/S0012-9593(01)01064-3, Ann. Sci. Éc. Norm. Supér, IV.  Sér. 34 (2001), 403–440. (2001) MR1839580DOI10.1016/S0012-9593(01)01064-3
  5. A letter to Stasheff, Gerstenhaber, May, Schechtman and Drinfeld, Unpublished, 1993. 
  6. Trees, free right-symmetric algebras, free Novikov algebras and identities, Homotopy Homology Appl. 4 (2002), 165–190. (2002) MR1918188
  7. The symmetric bar construction, Preprint, available from the author’s home page. 
  8. Distributive laws, bialgebras, and cohomology, Operads: Proceedings of Renaissance Conferences. Contemporary Math., Vol.  202, J.-L.  Loday, J. D.  Stasheff, and A. A.  Voronov (eds.), 1997, pp. 167–205. (1997) MR1436921
  9. 10.2307/1970343, Ann. Math. 78 (1963), 267–288. (1963) Zbl0131.27302MR0161898DOI10.2307/1970343
  10. Algebraic cohomology and deformation theory, In: Deformation Theory of Algebras and Structures and Applications, Kluwer, Dordrecht, 1988, pp. 11–264. (1988) MR0981619
  11. 10.1007/BF01077036, Funct. Anal. Appl. 29 (1995), 1–5. (Russian) (1995) MR1328534DOI10.1007/BF01077036
  12. Operads, homotopy algebra, and iterated integrals for double loop spaces, Preprint hep-th/9403055, March  1994. 
  13. 10.1215/S0012-7094-94-07608-4, Duke Math.  J. 76 (1994), 203–272. (1994) MR1301191DOI10.1215/S0012-7094-94-07608-4
  14. Tamarkin’s proof of Kontsevich formality theorem, Forum Mathematicum 15 (2003), 591–614. (2003) Zbl1081.16014MR1978336
  15. 10.1112/S0024611506015838, Proc. London Math. Soc. 93 (2006), 515–544. (2006) Zbl1103.55008MR2251161DOI10.1112/S0024611506015838
  16. On Kontsevich’s Hochschild cohomology conjecture, Compos. Math. 142 (2006), 143–168. (2006) MR2197407
  17. On spineless cacti, Deligne’s conjecture and Connes-Kreimer’s Hopf algebra, Preprint  math.QA/0308005, August  2003. Zbl1140.55008MR2288726
  18. 10.1007/BF00966559, Sib. Math.  J. 15 (1974), 914–920. (1974) DOI10.1007/BF00966559
  19. Simplicial localization of monoidal structures, and a non-linear version of Deligne’s conjecture, Compos. Math. 141 (2005), 253–261. (2005) MR2099778
  20. Deformations of algebras over operads and Deligne’s conjecture, Math. Phys. Stud. 21 (2000), 255–307. (2000) MR1805894
  21. Operads, Algebras, Modules and Motives. Astérisque, Vol.  233, Société Mathématique de France, 1995. (1995) MR1361938
  22. 10.1007/s10485-005-0911-2, Appl. Categorical Structures 13 (2005), 351–370. (2005) MR2175956DOI10.1007/s10485-005-0911-2
  23. 10.1016/0022-4049(95)00152-2, J.  Pure Appl. Algebra 113 (1996), 195–218. (1996) Zbl0865.18011MR1415558DOI10.1016/0022-4049(95)00152-2
  24. 10.1080/00927879608825647, Commun. Algebra 24 (1996), 1471–1500. (1996) Zbl0848.18003MR1380606DOI10.1080/00927879608825647
  25. The existence of intrinsic brackets on the cohomology of bialgebras, Preprint  math.AT/0411456, November  2004. 
  26. Operads in Algebra, Topology and Physics. Mathematical Surveys and Monographs, Vol. 96, American Mathematical Society, Providence, 2002. (2002) MR1898414
  27. The Geometry of Iterated Loop Spaces. Lecture Notes in Mathematics, Vol.  271, Springer-Verlag, New York, 1972. (1972) MR0420610
  28. A solution of Deligne’s Hochschild cohomology conjecture, In: Proceedings of the JAMI  conference on Homotopy Theory. Contemp. Math. Vol. 293, 2002, pp. 153–193. (2002) MR1890736
  29. 10.1090/S0894-0347-03-00419-3, J.  Am. Math. Soc. 16 (2003), 681–704. (2003) MR1969208DOI10.1090/S0894-0347-03-00419-3
  30. Configuration spaces with summable labels, In: Cohomological Methods in Homotopy Theory. Proceedings of the Barcelona conference on algebraic topology (BCAT), Bellaterra, Spain, June 4-10, 1998. Prog. Math.  196, J. Aguadé (ed.), Birkhäuser-Verlag, Basel, 2001, pp. 375–395. (2001) Zbl1034.55007MR1851264
  31. 10.1016/0022-4049(85)90019-2, J.  Pure Appl. Algebra 38 (1985), 313–322. (1985) MR0814187DOI10.1016/0022-4049(85)90019-2
  32. 10.1023/A:1010838604927, Lett. Math. Phys. 56 (2001), 85–97. (2001) MR1854129DOI10.1023/A:1010838604927
  33. Another proof of M. Kontsevich formality theorem, Preprint  math.QA/9803025, March  1998. 
  34. 10.1023/B:MATH.0000017651.12703.a1, Lett. Math. Phys. 66 (2003), 65–72. (2003) Zbl1048.18007MR2064592DOI10.1023/B:MATH.0000017651.12703.a1
  35. Operads up to homotopy and deformations of operad maps, Preprint  math.QA/0208041, August  2002. 
  36. Homotopy Gerstenhaber algebras, In: Conférence Moshé Flato  1999: Quantization, deformations, and symmetries, II. Math. Phys. Stud. Vol. 22, G. Dito (ed.), Kluwer Academic Publishers, Providence, 2000, pp. 307–331. (2000) Zbl0974.16005MR1805923

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