Geodesic
Lusternik–Schnirelmann category of spaces with free fundamental group
Strom, Jeffrey1
1Department of Mathematics, Western Michigan University, 1903 W. Michigan Ave., Kalamazoo, MI 49008
Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 1805-1808
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We find upper bounds for the Lusternik–Schnirelmann category of spaces with free fundamental groups. We prove, in particular, that if X is a finite-dimensional CW complex with a free fundamental group, then cat(X) ≤ 2 3 dim(X) + 1. Our results specialize to resolve a question about the L–S category of manifolds posed by Dranishnikov, Katz and Rudyak.

DOI : 10.2140/agt.2007.7.1805
Keywords: Lusternik–Schnirelmann category, fundamental group, manifold

Strom, Jeffrey  1

1 Department of Mathematics, Western Michigan University, 1903 W. Michigan Ave., Kalamazoo, MI 49008 
@article{10_2140_agt_2007_7_1805,
     author = {Strom, Jeffrey},
     title = {Lusternik{\textendash}Schnirelmann category of spaces with free fundamental group},
     journal = {Algebraic and Geometric Topology},
     pages = {1805--1808},
     year = {2007},
     volume = {7},
     number = {4},
     doi = {10.2140/agt.2007.7.1805},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.1805/}
}
TY  - JOUR
AU  - Strom, Jeffrey
TI  - Lusternik–Schnirelmann category of spaces with free fundamental group
JO  - Algebraic and Geometric Topology
PY  - 2007
SP  - 1805
EP  - 1808
VL  - 7
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.1805/
DO  - 10.2140/agt.2007.7.1805
ID  - 10_2140_agt_2007_7_1805
ER  - 
%0 Journal Article
%A Strom, Jeffrey
%T Lusternik–Schnirelmann category of spaces with free fundamental group
%J Algebraic and Geometric Topology
%D 2007
%P 1805-1808
%V 7
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.1805/
%R 10.2140/agt.2007.7.1805
%F 10_2140_agt_2007_7_1805
Strom, Jeffrey. Lusternik–Schnirelmann category of spaces with free fundamental group. Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 1805-1808. doi: 10.2140/agt.2007.7.1805

[1] O Cornea, G Lupton, J Oprea, D Tanré, Lusternik–Schnirelmann category, Mathematical Surveys and Monographs 103, American Mathematical Society (2003)

[2] A N Dranishnikov, M G Katz, Y B Rudyak, Small values of Lusternik–Schnirelmann and systolic categories for manifolds

[3] R Nendorf, N Scoville, J Strom, Categorical sequences, Algebr. Geom. Topol. 6 (2006) 809

[4] G W Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics 61, Springer (1978)

Cité par Sources :