Geodesic
The categorical sequence of a rational space
Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 49-71.

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

The categorical sequence of a space $X$ is a sequence of integers that encodes the growth of the Lusternik–Schnirelmann category of its $\textrm{CW}$ skeleta as dimension increases. Restrictions on these sequences found in “Categorical sequences” [R. Nendorf, N. Scoville, and J. Strom. Algebr. Geom. Topol., 6:809–838, 2006] have proven to be powerful tools in studying and computing $\textrm{L-S}$ category, motivating the search for additional restrictions. In this paper we study the initial three-term segments of the categorical sequences of rational spaces of finite type.We show that there is another restriction: a sequence of the form $(a, b, a + b, \dotsc)$ is the categorical sequence of a rational space of finite type if and only if $b \equiv 2 \: \mathrm{mod} \: a - 1$. With the possible exception of a small number of values of $c$ for each $a$, all other three-term initial sequences are realizable by simply-connected rational spaces of finite type.
DOI : 10.4310/HHA.2019.v21.n1.a3
Classification : 55M30, 55P62, 55Q15
Keywords: Lusternik–Schnirelmann category, rational homotopy theory 
@article{HHA_2019_21_1_a2,
     author = {Julienne Dare Houck and Jeffrey Strom},
     title = {The categorical sequence of a rational space},
     journal = {Homology, homotopy, and applications},
     pages = {49--71},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2019},
     doi = {10.4310/HHA.2019.v21.n1.a3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a3/}
}
TY  - JOUR
AU  - Julienne Dare Houck
AU  - Jeffrey Strom
TI  - The categorical sequence of a rational space
JO  - Homology, homotopy, and applications
PY  - 2019
SP  - 49
EP  - 71
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a3/
DO  - 10.4310/HHA.2019.v21.n1.a3
LA  - en
ID  - HHA_2019_21_1_a2
ER  - 
%0 Journal Article
%A Julienne Dare Houck
%A Jeffrey Strom
%T The categorical sequence of a rational space
%J Homology, homotopy, and applications
%D 2019
%P 49-71
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a3/
%R 10.4310/HHA.2019.v21.n1.a3
%G en
%F HHA_2019_21_1_a2
Julienne Dare Houck; Jeffrey Strom. The categorical sequence of a rational space. Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 49-71. doi : 10.4310/HHA.2019.v21.n1.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a3/

Cité par Sources :