Geodesic
Framed Stratified Sets in Morse Theory
Canadian journal of mathematics, Tome 54 (2002) no. 2, pp. 396-416

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we present a smooth framework for some aspects of the “geometry of CW complexes”, in the sense of Buoncristiano, Rourke and Sanderson. We then apply these ideas to Morse theory, in order to generalize results of Franks and Iriye-Kono.More precisely, consider a Morse function $f$ on a closed manifold $M$ . We investigate the relations between the attaching maps in a $\text{CW}$ complex determined by $f$ , and the moduli spaces of gradient flow lines of $f$ , with respect to some Riemannian metric on $M$ .
DOI : 10.4153/CJM-2002-013-7
Mots-clés : 57R70, 57N80, 55N45 
Lebel, André. Framed Stratified Sets in Morse Theory. Canadian journal of mathematics, Tome 54 (2002) no. 2, pp. 396-416. doi: 10.4153/CJM-2002-013-7
@article{10_4153_CJM_2002_013_7,
     author = {Lebel, Andr\'e},
     title = {Framed {Stratified} {Sets} in {Morse} {Theory}},
     journal = {Canadian journal of mathematics},
     pages = {396--416},
     year = {2002},
     volume = {54},
     number = {2},
     doi = {10.4153/CJM-2002-013-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2002-013-7/}
}
TY  - JOUR
AU  - Lebel, André
TI  - Framed Stratified Sets in Morse Theory
JO  - Canadian journal of mathematics
PY  - 2002
SP  - 396
EP  - 416
VL  - 54
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2002-013-7/
DO  - 10.4153/CJM-2002-013-7
ID  - 10_4153_CJM_2002_013_7
ER  - 
%0 Journal Article
%A Lebel, André
%T Framed Stratified Sets in Morse Theory
%J Canadian journal of mathematics
%D 2002
%P 396-416
%V 54
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2002-013-7/
%R 10.4153/CJM-2002-013-7
%F 10_4153_CJM_2002_013_7

[1] [1] Austin, D. M. and Braam, P. J., Morse-Bott theory and equivariant cohomology. Preprint, 1994. Google Scholar

[2] [2] Buoncristiano, S. and Dedo, M., Local blow-up of stratified sets up to bordism. Trans. Amer. Math. Soc. 273 (1982), 253–280. Google Scholar

[3] [3] Buoncristiano, S., Rourke, C. P. and Sanderson, B. J., A geometric approach to homology theory. Cambridge University Press, 1976. Google Scholar

[4] [4] Cohen, R. L., Jones, J. D. S. and Segal, G. B., Morse theory and classifying spaces. Preprint, 1992. Google Scholar

[5] [5] Franks, J., Morse-Smale flows and homotopy theory. Topology 18 (1979), 199–215. Google Scholar

[6] [6] Goresky, M., Whitney stratified chains and cochains. Trans. Amer. Math. Soc. 267 (1981), 175–196. Google Scholar

[7] [7] Hirsch, M., Differential Topology. Springer, 1976. Google Scholar

[8] [8] Iriye, K. and Kono, A., Morse function and attaching map. J. Math. Kyoto Univ. (1) 35 (1995), 79–83. Google Scholar

[9] [9] Lebel, A., Framed stratified sets in Morse theory. Ph.D. thesis, University of Warwick, 1996. Google Scholar

[10] [10] Schwartz, M., Morse Homology. Birkhauser, 1993. Google Scholar

[11] [11] Smale, S., On gradient dynamical systems. Ann. of Maths. 74 (1961), 199–206. Google Scholar

[12] [12] Verona, A., Stratified mappings—Structure and Triangulability. Lecture Notes in Math. 1102, Springer-Verlag, 1984. Google Scholar

Cité par Sources :