Free crossed resolutions from simplicial resolutions with given C W -basis

A. Mutlu; T. Porter

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1999)

  • Volume: 40, Issue: 4, page 261-283
  • ISSN: 1245-530X

How to cite

top

Mutlu, A., and Porter, T.. "Free crossed resolutions from simplicial resolutions with given $CW$-basis." Cahiers de Topologie et Géométrie Différentielle Catégoriques 40.4 (1999): 261-283. <http://eudml.org/doc/91623>.

@article{Mutlu1999,
author = {Mutlu, A., Porter, T.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {crossed complex; Moore complex; simplicial group; simplicial resolution},
language = {eng},
number = {4},
pages = {261-283},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Free crossed resolutions from simplicial resolutions with given $CW$-basis},
url = {http://eudml.org/doc/91623},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Mutlu, A.
AU - Porter, T.
TI - Free crossed resolutions from simplicial resolutions with given $CW$-basis
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1999
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 40
IS - 4
SP - 261
EP - 283
LA - eng
KW - crossed complex; Moore complex; simplicial group; simplicial resolution
UR - http://eudml.org/doc/91623
ER -

References

top
  1. [1] M. André, Homologie des Algèbre Commutatives, Lecture Notes in Math., Springer, 206, (1970). Zbl0222.13017MR352220
  2. [2] N. Ashley, Simplicial T.-Complexes: a non abelian version of a theorem of Dold-Kan, Dissertationes Math., 165, (1988), 11-58, Ph.D. Thesis, University of Wales, Bangor, (1978). Zbl1003.55500
  3. [3] H.J. Baues, Algebraic Homotopy, Cambridge Studies in Advanced Mathematics, 15, Cambridge Univ. Press., (1989), 450 pages. Zbl0688.55001MR985099
  4. [4] R. Brown, M. Golasi, T. Porter, and A. Tonks, Spaces of maps into classifying spaces for equivariant crossed complexes, Indag. Mathem., N.S.8(2), (1997), 157-172. Zbl0898.55009MR1621979
  5. [5] R. Brown and P.J. Higgins, Colimit-theorems for relative homotopy groups, Jour. Pure Appl. Algebra, 22, (1981), 11-41. Zbl0475.55009MR621285
  6. [6] R. Brown and P.J. Higgins, Homotopies and tensor products for ω-groupoids and crossed complexes, Jour. Pure Appl. Algebra, 47, (1987), 1-33. Zbl0621.55009
  7. [7] R. Brown and J. Huesbschmann, Identities among relations, Low dimension topology, London Math. Soc. Lecture Note Series, 48, (ed. R. Brown and T. L. Thickstun, Cambridge University Press) 1982, pp. 153-202. Zbl0485.57001MR662431
  8. [8] R. Brown and J.-L. Loday, Van Kampen Theorems for Diagram of Spaces, Topology, 26, (1987), 311-335. Zbl0622.55009MR899052
  9. [9] R.A. Brown, Generalized Group Presentations and Formal Deformations of CW complexes, Trans. Amer. Math. Soc.334, (1992), 519-549. Zbl0764.57012MR1153010
  10. [10] P. Carrasco, Complejos Hipercruzados, Cohomologia y Extensiones, Ph.D. Thesis, Universidad de Granada, (1987). 
  11. [11] P. Carrasco and A.M. Cegarra, Group-theoretic Algebraic Models for Homotopy Types, Jour. Pure Appl. Algebra, 75, (1991), 195-235. Zbl0742.55003MR1137837
  12. [12] D. Conduché, Modules Croisés Généralisés de Longueur 2, Jour. Pure Appl. Algebra, 34, (1984), 155-178. Zbl0554.20014MR772056
  13. [13] E.B. Curtis, Simplicial Homotopy Theory, Advances in Math., 6, (1971), 107-209. Zbl0225.55002MR279808
  14. [14] P.J. Ehlers and T. Porter, Varieties of Simplicial Groupoids, I: Crossed Complexes. Jour. Pure Appl. Algebra, 120, (1997), 221-233; plus: Correction, same journal (to appear). Zbl0888.55005MR1468917
  15. [15] D.M. Kan, A relation between CW-complexes and free c.s.s groups, Amer. Jour. Maths., 81, (1959), 512-528. Zbl0109.16201MR111036
  16. [16] F. Keune, Homotopical Algebra and Algebraic K-theory, Thesis, Universiteit van Amsterdam, 1972. 
  17. [17] J.P. May, Simplicial Objects in Algebraic Topology, Van Nostrand, Math. Studies, 11, (1967). Zbl0165.26004MR222892
  18. [18] J.C. Moore, Seminar in Algebraic Homotopy, Princeton, (1956). Zbl0074.38401
  19. [19] A. Mutlu, Peiffer Pairings in the Moore Complex of a Simplicial Group, Ph.D. Thesis, University of Wales, Bangor, (1997); Bangor Preprint, 97.11, available via http://www.bangor.ac.uk/ma/research/preprints/97prep.html Zbl0917.18006
  20. [20] A. Mutlu and T. Porter, Iterated Peiffer pairings in the Moore complex of a simplicial group, Applied Categorical Structures (to appear); (1997), Bangor Preprint, 97.12, available via http://www.bangor.ac.uk/ma/research/preprints/97prep.html Zbl0991.18012MR1812299
  21. [21] A. Mutlu and T. Porter, Applications of Peiffer pairings in the Moore complex of a simplicial group, Theory and Applications of Categories, 4, No. 7, (1998) 148-173; previously as Bangor. Preprint 97.17. available via http://www.bangor.ac.uk/ma/research/preprints/97prep.htmt. Zbl0917.18006MR1660886
  22. [22] A. Mutlu and T. Porter, Freeness Conditions for 2-Crossed Modules and Complexes, Theory and Applications of Categories, 4, No.8, (1998) 174-194; previously as Bangor Preprint 97.19. available via http://www.bangor.ac.uk/ma/research/preprints/97prep.htm). Zbl0917.18004MR1657199
  23. [23] T. Porter, n-Types of simplicial groups and crossed n-cubes, Topology, 32, (1993), 5-24. Zbl0776.55012MR1204402
  24. [24] D. Quillen, Homotopical Algebra, Lecture Notes in Math., Springer, 43, (1967). Zbl0168.20903MR223432
  25. [25] A.P. Tonks, Theory and Applications of crossed complexes, Ph.D. Thesis, University of Wales, Bangor, (1993). 
  26. [26] J.H.C. Whitehead, Combinatorial Homotopy I and II, Bull. Amer. Math. Soc., 55, (1949), 231-245 and 453-496. Zbl0040.38801MR30760

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.