Cochains and homotopy type

Michael A. Mandell

Publications Mathématiques de l'IHÉS (2006)

  • Volume: 103, page 213-246
  • ISSN: 0073-8301

Abstract

top
Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.

How to cite

top

Mandell, Michael A.. "Cochains and homotopy type." Publications Mathématiques de l'IHÉS 103 (2006): 213-246. <http://eudml.org/doc/104217>.

@article{Mandell2006,
abstract = {Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.},
author = {Mandell, Michael A.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {homotopy type; -algebra; singular cochains; arithmetic square},
language = {eng},
pages = {213-246},
publisher = {Springer},
title = {Cochains and homotopy type},
url = {http://eudml.org/doc/104217},
volume = {103},
year = {2006},
}

TY - JOUR
AU - Mandell, Michael A.
TI - Cochains and homotopy type
JO - Publications Mathématiques de l'IHÉS
PY - 2006
PB - Springer
VL - 103
SP - 213
EP - 246
AB - Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.
LA - eng
KW - homotopy type; -algebra; singular cochains; arithmetic square
UR - http://eudml.org/doc/104217
ER -

References

top
  1. 1. A. K. Bousfield, The localization of spaces with respect to homology, Topology, 14 (1975), 133–150. Zbl0309.55013MR380779
  2. 2. E. Dror, A generalization of the Whitehead theorem, Symposium on Algebraic Topology (Battelle Seattle Res. Center, Seattle, WA 1971), Lect. Notes Math., vol. 249, Springer, Berlin, 1971, pp. 13–22. Zbl0243.55018MR350725
  3. 3. W. G. Dwyer and D. M. Kan, Simplicial localizations of categories, J. Pure Appl. Algebra, 17 (1980), 267–284. Zbl0485.18012MR579087
  4. 4. W. G. Dwyer and D. M. Kan, Calculating simplicial localizations, J. Pure Appl. Algebra, 18 (1980), 17–35. Zbl0485.18013MR578563
  5. 5. W. G. Dwyer and D. M. Kan, Function complexes in homotopical algebra, Topology, 19 (1980), 427–440. Zbl0438.55011MR584566
  6. 6. W. G. Dwyer and J. Spaliński, Homotopy theories and model categories, Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 73–126. Zbl0869.55018MR1361887
  7. 7. V. Hinich, Virtual operad algebras and realization of homotopy types, J. Pure Appl. Algebra, 159 (2001), 173–185. Zbl0992.18007MR1828937
  8. 8. M. A. Mandell, Equivalence of simplicial localizations of closed model categories, J. Pure Appl. Algebra, 142 (1999), 131–152. Zbl0938.55030MR1715404
  9. 9. M. A. Mandell, E∞ algebras and p-adic homotopy theory, Topology, 40 (2001), 43–94. Zbl0974.55004
  10. 10. M. A. Mandell, Equivariant p-adic homotopy theory, Topology Appl., 122 (2002), 637–651. Zbl1003.55003MR1911706
  11. 11. J. P. May, Simplicial objects in algebraic topology, D. Van Nostrand Co., Inc., Princeton, NJ – Toronto, ON – London, 1967. Zbl0165.26004MR222892
  12. 12. D. G. Quillen, Homotopical algebra, Lect. Notes Math., vol. 43, Springer, Berlin, 1967. Zbl0168.20903MR223432
  13. 13. D. G. Quillen, Rational homotopy theory, Ann. Math., 90 (1969), 205–295. Zbl0191.53702MR258031
  14. 14. J.-P. Serre, Local fields, Springer, New York, 1979. Translated from the French by M. J. Greenberg. Zbl0423.12016MR554237
  15. 15. V. A. Smirnov, Homotopy theory of coalgebras, Math. USSR–Izv., 27 (1986), 575–592. Zbl0612.55012MR816858
  16. 16. J. R. Smith, Operads and algebraic homotopy, preprint math.AT/0004003. 
  17. 17. D. Sullivan, The genetics of homotopy theory and the Adams conjecture, Ann. Math., 100 (1974), 1–79. Zbl0355.57007MR442930
  18. 18. D. Sullivan, Infinitesimal computations in topology, Publ. Math., Inst. Hautes Étud. Sci., 47 (1978), 269–331. Zbl0374.57002MR646078

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.