Geodesic
Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
Homology, homotopy, and applications, Tome 18 (2016) no. 2, pp. 233-245.

Voir la notice de l'article provenant de la source International Press of Boston

We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason’s theorem on homotopy colimits over posets. In particular, this allows us to characterize the homotopy colimits of diagrams of simplicial complexes in terms of the Grothendieck construction on the diagrams of their face posets. We also derive analogues of well known results on homotopy colimits in the combinatorial setting, including a cofinality theorem and a generalization of Quillen’s Theorem A for posets.
DOI : 10.4310/HHA.2016.v18.n2.a13
Classification : 06A06, 18A30, 18B35, 55P15, 55U10
Keywords: homotopy colimit, finite topological space, poset, Grothendieck construction, Quillen’s Theorem A 
@article{HHA_2016_18_2_a12,
     author = {Ximena Fern\'andez and El{\'\i}as Gabriel Minian},
     title = {Homotopy colimits of diagrams over posets and variations on a theorem of {Thomason}},
     journal = {Homology, homotopy, and applications},
     pages = {233--245},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2016},
     doi = {10.4310/HHA.2016.v18.n2.a13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n2.a13/}
}
TY  - JOUR
AU  - Ximena Fernández
AU  - Elías Gabriel Minian
TI  - Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
JO  - Homology, homotopy, and applications
PY  - 2016
SP  - 233
EP  - 245
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n2.a13/
DO  - 10.4310/HHA.2016.v18.n2.a13
LA  - en
ID  - HHA_2016_18_2_a12
ER  - 
%0 Journal Article
%A Ximena Fernández
%A Elías Gabriel Minian
%T Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
%J Homology, homotopy, and applications
%D 2016
%P 233-245
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n2.a13/
%R 10.4310/HHA.2016.v18.n2.a13
%G en
%F HHA_2016_18_2_a12
Ximena Fernández; Elías Gabriel Minian. Homotopy colimits of diagrams over posets and variations on a theorem of Thomason. Homology, homotopy, and applications, Tome 18 (2016) no. 2, pp. 233-245. doi : 10.4310/HHA.2016.v18.n2.a13. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n2.a13/

Cité par Sources :