## The (1998)

### BibTeX

@MISC{Brown98the,

author = {R Brown and M Golasiński and T Porter and A Tonks},

title = {The},

year = {1998}

}

### OpenURL

### Abstract

Spaces of maps into classifying spaces for equivariant crossed complexes, II:

### Citations

307 |
Homotopy limits, completions and localizations
- Bousfield, Kan
- 1972
(Show Context)
Citation Context ...p), B(FA0, GAp)), A0,...,Ap where the cosimplicial variation comes from the nerve-like indexation in the first place of the simplicial mapping space. The total space construction of Bousfield and Kan =-=[2]-=- gives ∫ Coh(A, B)(F, G) = S(∆[p], Y (F, G) p ). Thus with this description a h.c. transformation φ of dimension n can be specified by a family { φA0,...,Ap : A(A0, A1) × · · · × A(Ap−1, Ap) × ∆[p] × ... |

71 |
Cohomologie cyclique et foncteurs Ext n
- Connes
- 1983
(Show Context)
Citation Context ...eas for applications of our results it excludes some important instances of group actions, for example actions of the circle group. Inclusion of this case would allow us to handle Connes’ cyclic sets =-=[7]-=- since it is known that the homotopy theory of cyclic sets is equivalent to that of circle actions (cf. [13, 18]). This in turn would open up a large area to the techniques of algebraic homotopy givin... |

43 | The classifying space of a crossed complex - Brown, Higgins |

26 | Systems of fixed point sets - Elmendorf - 1983 |

22 | Homotopy Coherent Category Theory
- Cordier, Porter
(Show Context)
Citation Context ...treatment in [19]. Once this is done we will make the necessary changes to translate the coherence to the S-enriched form that is needed so as to apply more easily the technical machinery of [10] and =-=[11]-=-. If K, L are simplicial sets, then there is a simplicial map given in dimension n by φK,L : S(K, L) → Crs(πK, πL) φK,L(f : K × ∆[n] → L) := (π(K) ⊗ π(n) b −→ π(K × ∆[n]) π(f) −→ π(L)) As noted earlie... |

20 |
T.: Vogt’s theorem on categories of homotopy coherent diagrams
- Cordier, Porter
- 1986
(Show Context)
Citation Context ...2) × ∆[1] −→ Crs(πK0, πK2). (8) Thus π induces a functor at the homotopy category level. However much more is true: π induces a homotopy coherent functor in a sense we explain next. 13Recall ([8] or =-=[9]-=-) that the category, Cat, of small categories has a forgetful functor to the category of directed graphs. This functor has a left adjoint (the free category on the directed graph) and using this adjoi... |

19 | Crossed simplicial groups and their associated homology
- Feidorowicz, Loday
- 1991
(Show Context)
Citation Context ... to that of circle actions (cf. [13, 18]). This in turn would open up a large area to the techniques of algebraic homotopy giving a wide range of potential applications. Work by Loday and Fiedorowicz =-=[15]-=-, Aboughazi [1], Burghelea, Fiedorowicz and Gajda [6] suggests that various other important cases, such as G∗-spaces for a crossed simplicial group G∗, epicyclic spaces, etc., may lead to similar well... |

13 |
la notion de diagramme homotopiquement cohérent. Cahiers Topologie Géom. Différentielle 23
- Cordier
- 1982
(Show Context)
Citation Context ...S(K1, K2) × ∆[1] −→ Crs(πK0, πK2). (8) Thus π induces a functor at the homotopy category level. However much more is true: π induces a homotopy coherent functor in a sense we explain next. 13Recall (=-=[8]-=- or [9]) that the category, Cat, of small categories has a forgetful functor to the category of directed graphs. This functor has a left adjoint (the free category on the directed graph) and using thi... |

10 | Spaces of maps into classifying spaces for equivariant crossed complexes
- Brown, Golasiński, et al.
- 1997
(Show Context)
Citation Context ...olas Copernicus, Torun, Poland 3 Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Cerdanyola, Barcelona, Catalunya, Spain August 19, 1998 Abstract The results of a previous paper =-=[3]-=- on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis... |

9 | D.M.: Singular functors and realization functors - Dwyer, Kan - 1984 |

8 |
The homotopy theory of cyclic sets
- Dwyer, Hopkins, et al.
- 1985
(Show Context)
Citation Context ...ons of the circle group. Inclusion of this case would allow us to handle Connes’ cyclic sets [7] since it is known that the homotopy theory of cyclic sets is equivalent to that of circle actions (cf. =-=[13, 18]-=-). This in turn would open up a large area to the techniques of algebraic homotopy giving a wide range of potential applications. Work by Loday and Fiedorowicz [15], Aboughazi [1], Burghelea, Fiedorow... |

7 |
Equivariant Eilenberg-Mac Lane spaces K(G,µ,1) for possibly non-connected or empty fixed point sets
- Lück
- 1987
(Show Context)
Citation Context ...lexes concentrating on the construction of an equivariant classifying space. The use of crossed complexes allowed us to include as special cases previous work on equivariant Eilenberg-Mac Lane spaces =-=[16]-=-, including the case of dimension 1, and work on local systems. Another special case was the theory of equivariant 2-types due to Moerdijk and Svensson [17]. Significantly, our methods gave results no... |

4 | Categorical Aspects of Equivariant Homotopy
- Cordier, Porter
- 1996
(Show Context)
Citation Context ...category of OrG op -diagrams of simplicial sets via a singular S-functor R : G-Top → S OrGop and a ‘coalescence’ or ‘realisation’ functor c : S OrGop → G-Top which together form an adjoint pair as in =-=[10]-=-. Here OrG is the simplicially enriched orbit category of G where for subgroups H, H ′ of G, i.e. in dimension n OrG(G/H, G/H ′ ) = G-Top(G/H, G/H ′ ), OrG(G/H, G/H ′ )n = G-Top(G/H × ∆ n , G/H ′ ), w... |

4 |
Algebraic classification of equivariant 2-types
- Moerdijk, Svensson
- 1993
(Show Context)
Citation Context ...rk on equivariant Eilenberg-Mac Lane spaces [16], including the case of dimension 1, and work on local systems. Another special case was the theory of equivariant 2-types due to Moerdijk and Svensson =-=[17]-=-. Significantly, our methods gave results not just on the homotopy classification of maps but also on the (weak) homotopy types of certain function spaces of equivariant maps. The convenient propertie... |

3 |
Power maps and epicyclic spaces
- Burghelea, Fiedorowicz, et al.
- 1994
(Show Context)
Citation Context ...n would open up a large area to the techniques of algebraic homotopy giving a wide range of potential applications. Work by Loday and Fiedorowicz [15], Aboughazi [1], Burghelea, Fiedorowicz and Gajda =-=[6]-=- suggests that various other important cases, such as G∗-spaces for a crossed simplicial group G∗, epicyclic spaces, etc., may lead to similar well-structured examples, and this without touching on ge... |

2 |
Groupes simplicial croisés, p-algèbres de Lie, produit tensoriel du groupe d’Heisenberg, Thèse, Université Louis Pasteur
- Aboughazi
- 1987
(Show Context)
Citation Context ...le actions (cf. [13, 18]). This in turn would open up a large area to the techniques of algebraic homotopy giving a wide range of potential applications. Work by Loday and Fiedorowicz [15], Aboughazi =-=[1]-=-, Burghelea, Fiedorowicz and Gajda [6] suggests that various other important cases, such as G∗-spaces for a crossed simplicial group G∗, epicyclic spaces, etc., may lead to similar well-structured exa... |

1 |
Strong homotopy theory of cyclic sets’, J. Pure Applied Algebra 99
- Spalinski
- 1995
(Show Context)
Citation Context ...ons of the circle group. Inclusion of this case would allow us to handle Connes’ cyclic sets [7] since it is known that the homotopy theory of cyclic sets is equivalent to that of circle actions (cf. =-=[13, 18]-=-). This in turn would open up a large area to the techniques of algebraic homotopy giving a wide range of potential applications. Work by Loday and Fiedorowicz [15], Aboughazi [1], Burghelea, Fiedorow... |