Sectional category à la Quillen
DOI:
https://doi.org/10.12775/TMNA.2024.054Słowa kluczowe
Rational homotopy theory, sectional category, Quillen modelsAbstrakt
In this note we give a characterization of the sectional category of a map between rational spaces in terms of its Koszul-Quillen model.Bibliografia
I. Berstein and T. Ganea, The category of a map and of a cohomology class, Fund. Math., 50 (1962), no. 3, 265–279.
J.G. Carrasquel-Vera, The rational sectional category of certain maps, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 17 (2017), no. 2, 805–813.
N. Dupont, A counterexample of the Lemaire–Sigrist conjecture, Topology 38 (1999), no. 1, 189–196.
M. Farber, Topological complexity of motion planning Discrete Comput. Geom. 29 (2003), no. 2, 211–221.
Y. Félix and S. Halperin, Rational L.-S. category and its applications, Trans. Amer. Math. Soc. 273 (1982), no. 1, 1–37.
Y. Félix, S. Halperin and J.-C. Thomas, Rational Homotopy Theory, Graduate Texts in Mathematics, vol. 205, Spinger, 2000.
R.H. Fox, On the Lusternik–Schnirelmann category, Ann. of Math. 42 (1941), 333–370.
J.-M. Lemaire and F. Sigrist, Sur les invariants d’homotopie rationnelle lié s à la L.S. category, Comment. Math. Helv. 56 (1981), 103–122.
G. Lupton and S.B. Smith, Rationalized evaluation subgroups of a map II: Quillen models and adjoint maps, J. Pure Appl. Algebra 209 (2007), no. 1, 173–188.
L. Lusternik and L. Schnirelmann, Méthodes topologiques dans les problèmes variationnels, vol. 188, Hermann, Paris, 1934.
D. Quillen, Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205–295.
A. S. Schwarz, The genus of a fiber space, Amer. Math. Sci. Transl. 55 (1966), 49–140.
D. Sullivan, Infinitesimal computations in topology, Publications Mathématiques de l’IHÉS 47 (1977), 269–331.
D. Tanré, Homotopie Rationnelle: Modèles de Chen, Quillen, Sullivan, Lecture Notes in Math., vol. 1025, Springer, 1983.
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Statystyki
Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0
