Injective models of G -disconnected simplicial sets

Marek Golasiński

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 5, page 1491-1522
  • ISSN: 0373-0956

Abstract

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We generalize the results by G.V. Triantafillou and B. Fine on G -disconnected simplicial sets. An existence of an injective minimal model for a complete 𝕀 -algebra is presented, for any E I -category 𝕀 . We then make use of the E I -category 𝒪 ( G , X ) associated with a G -simplicial set X to apply these results to the category of G -simplicial sets.Finally, we describe the rational homotopy type of a nilpotent G -simplicial set by means of its injective minimal model.

How to cite

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Golasiński, Marek. "Injective models of $G$-disconnected simplicial sets." Annales de l'institut Fourier 47.5 (1997): 1491-1522. <http://eudml.org/doc/75271>.

@article{Golasiński1997,
abstract = {We generalize the results by G.V. Triantafillou and B. Fine on $G$-disconnected simplicial sets. An existence of an injective minimal model for a complete $\{\Bbb I\}$-algebra is presented, for any $EI$-category $\{\Bbb I\}$. We then make use of the $EI$-category $\{\cal O\}(G,X)$ associated with a $G$-simplicial set $X$ to apply these results to the category of $G$-simplicial sets.Finally, we describe the rational homotopy type of a nilpotent $G$-simplicial set by means of its injective minimal model.},
author = {Golasiński, Marek},
journal = {Annales de l'institut Fourier},
keywords = {differential graded algebra; de Rham algebra; -category; Grothendieck construction; -minimal model; linearly compact (complete); -module; Postnikov tower; simplicial set; injective model; equivariant homotopy theory; simplicial object},
language = {eng},
number = {5},
pages = {1491-1522},
publisher = {Association des Annales de l'Institut Fourier},
title = {Injective models of $G$-disconnected simplicial sets},
url = {http://eudml.org/doc/75271},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Golasiński, Marek
TI - Injective models of $G$-disconnected simplicial sets
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 5
SP - 1491
EP - 1522
AB - We generalize the results by G.V. Triantafillou and B. Fine on $G$-disconnected simplicial sets. An existence of an injective minimal model for a complete ${\Bbb I}$-algebra is presented, for any $EI$-category ${\Bbb I}$. We then make use of the $EI$-category ${\cal O}(G,X)$ associated with a $G$-simplicial set $X$ to apply these results to the category of $G$-simplicial sets.Finally, we describe the rational homotopy type of a nilpotent $G$-simplicial set by means of its injective minimal model.
LA - eng
KW - differential graded algebra; de Rham algebra; -category; Grothendieck construction; -minimal model; linearly compact (complete); -module; Postnikov tower; simplicial set; injective model; equivariant homotopy theory; simplicial object
UR - http://eudml.org/doc/75271
ER -

References

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  15. [15] G.V. TRIANTAFILLOU, An algebraic model for G-homotopy types, Astérisque, 113-114 (1984), 312-337. Zbl0564.55009MR85m:55009

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