The double bar and cobar constructions

H. J. Baues

Compositio Mathematica (1981)

  • Volume: 43, Issue: 3, page 331-341
  • ISSN: 0010-437X

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Baues, H. J.. "The double bar and cobar constructions." Compositio Mathematica 43.3 (1981): 331-341. <http://eudml.org/doc/89505>.

@article{Baues1981,
author = {Baues, H. J.},
journal = {Compositio Mathematica},
keywords = {Bar construction; double loop space; iterated cobar construction},
language = {eng},
number = {3},
pages = {331-341},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {The double bar and cobar constructions},
url = {http://eudml.org/doc/89505},
volume = {43},
year = {1981},
}

TY - JOUR
AU - Baues, H. J.
TI - The double bar and cobar constructions
JO - Compositio Mathematica
PY - 1981
PB - Sijthoff et Noordhoff International Publishers
VL - 43
IS - 3
SP - 331
EP - 341
LA - eng
KW - Bar construction; double loop space; iterated cobar construction
UR - http://eudml.org/doc/89505
ER -

References

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  1. [1] J.F. Adams: On the cobar construction. Proc. Nat. Acad. Sci. (USA) 42 (1956) 409-412. Zbl0071.16404MR79266
  2. [2] J.F. Adams, and P.J. Hilton: On the chain algebra of a loop space. Comment. Math. Helv.30 (1956), 305-330. Zbl0071.16403MR77929
  3. [3] H.J. Baues: Geometry of loop spaces and the cobar construction. Memoirs of the AMS25 (1980) 230 ISSN 0065-9266. Zbl0473.55009MR567799
  4. [4] A.K. Bousfield and V.K.A.M. Gugenheim: On PL de Rham theory and rational homotopy type. Memoirs of the AMS179 (1976). Zbl0338.55008MR425956
  5. [5] A. Dold and R. Lashof: Principal quasifibrings and fiber homotopy equivalence of bundles. Ill. J. Math.3 (1959), 285-305. Zbl0088.15301MR101521
  6. [6] B. Drachman: A diagonal map for the cobar construction. Bol. Soc. Mat. Mexicana (2) 12 (1967) 81-91. Zbl0185.51002MR239594
  7. [7] D. Husemoller, J.C. Moore and J. Stasheff: Differential homological algebra and homogeneous spaces. J. pure appl. Algebra5 (1974) 113-185. Zbl0364.18008MR365571
  8. [8] J.R. Milgram: The bar construction and abelian H-spaces. Ill. J. Math.11 (1967) 242-250. Zbl0152.40502MR208595
  9. [9] J.R. Milgram: Iterated loop spaces. Ann. of Math.84 (1966) 386-403. Zbl0145.19901MR206951
  10. [10] J. Milnor and J.C. Moore: On the structure of Hopf algebras. Ann. Math.81 (1965) 211-264. Zbl0163.28202MR174052
  11. [11] J.C. Moore: Differential homological algebra. Actes du Congr. Intern. des Mathématiciens (1970) 335-336. Zbl0337.18009MR436178
  12. [12] H.J. Munkholm: The Eilenberg-Moore spectral sequence and strongly homotopy multiplicative maps. J. pure and appl. Algebra5 (1974) 1-50. Zbl0294.55011MR350735
  13. [13] L. Smith: Homological algebra and the Eilenberg-Moore spectral sequence. Trans. of AMS129 (1967) 58-93. Zbl0177.51402MR216504

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