Homotopical dynamics II : Hopf invariants, smoothings and the Morse complex
Annales scientifiques de l'École Normale Supérieure (2002)
- Volume: 35, Issue: 4, page 549-573
- ISSN: 0012-9593
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topCornea, Octavian. "Homotopical dynamics II : Hopf invariants, smoothings and the Morse complex." Annales scientifiques de l'École Normale Supérieure 35.4 (2002): 549-573. <http://eudml.org/doc/82582>.
@article{Cornea2002,
author = {Cornea, Octavian},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Morse complex; Hopf invariant; framed bordism; non-smoothable Poincaré duality spaces},
language = {eng},
number = {4},
pages = {549-573},
publisher = {Elsevier},
title = {Homotopical dynamics II : Hopf invariants, smoothings and the Morse complex},
url = {http://eudml.org/doc/82582},
volume = {35},
year = {2002},
}
TY - JOUR
AU - Cornea, Octavian
TI - Homotopical dynamics II : Hopf invariants, smoothings and the Morse complex
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2002
PB - Elsevier
VL - 35
IS - 4
SP - 549
EP - 573
LA - eng
KW - Morse complex; Hopf invariant; framed bordism; non-smoothable Poincaré duality spaces
UR - http://eudml.org/doc/82582
ER -
References
top- [1] Adams F., On the groups J(X). IV, Topology5 (1966) 21-71. Zbl0145.19902MR198470
- [2] Agoston M.K., On handle decompositions and diffeomorphisms, Trans. Amer. Math. Soc.137 (1969) 21-26. Zbl0176.21603MR236938
- [3] Arkowitz M., The generalized Whitehead product, Pacific J. Math.12 (1962) 7-23. Zbl0118.18404MR155328
- [4] Cohen R.L., Jones J.D.S., Segal G.B., Morse theory and classifying spaces, Preprint.
- [5] Cohen R., Jones J.D.S., Segal G., Floer's Infinite Dimensional Morse Theory and Homotopy Theory, The Floer Memorial Volume, Birkhauser, 1995. Zbl0843.58019MR1362832
- [6] Cornea O., Homotopical dynamics: suspension and duality, Ergodic Theory Dynamical Systems20 (2000) 379-391. Zbl0984.37017MR1756976
- [7] Cornea O., Spanier–Whitehead duality and critical points, in: Homotopy Theory via Algebraic Geometry and Group Representations, Contemp. Math., 220, American Mathematical Society, 1998, pp. 47-63. Zbl0911.55004MR1642889
- [8] Cornea O., Cone-decompositions and degenerate critical points, Proc. London Math. Soc.77 (1998) 437-461. Zbl0913.55002MR1635165
- [9] Dula G., On conic spaces, in: Lecture Notes in Math., 1474, Springer, 1991, pp. 38-58. Zbl0793.55001MR1133891
- [10] Eells J., Kuiper N.H., Manifolds which are like projective planes, Pub. IHES14 (1962) 5-46. Zbl0109.15701MR145544
- [11] Franks J., Morse–Smale flows and homotopy theory, Topology18 (1979) 199-215. Zbl0426.58013MR546790
- [12] Ganea T., Cogroups and suspension, Invent. Math.9 (1970) 185-197. Zbl0194.55103MR267582
- [13] Ganea T., A generalization of the homology and homotopy suspension, Comment. Math. Helv.39 (1965) 295-322. Zbl0142.40702MR179791
- [14] Iwase N., Ganea's conjecture on the Lusternik–Schnirelmann category, Bull. London Math. Soc.30 (1998) 623-634. Zbl0947.55006MR1642747
- [15] Kahn D., Priddy S., Applications of the transfer to stable homotopy, Bull. Amer. Math. Soc.78 (1972) 981-987. Zbl0265.55009MR309109
- [16] Kervaire M., A manifold which does not admit any differentiable structure, Comment. Math. Helv.34 (1960) 257-270. Zbl0145.20304MR139172
- [17] Kervaire M., Milnor J., Groups of homotopy spheres. I, Ann. of Math.77 (1963) 504-537. Zbl0115.40505MR148075
- [18] Klein J., Higher Reidemeister torsion and parametrized Morse theory, Rend. Circ. Mat. Palermo (2) Suppl.30 (1993) 15-20. Zbl0807.57026MR1246615
- [19] Klein J., Poincaré duality embeddings and fiberwise homotopy theory, Topology, to appear. Zbl0928.57028MR1670412
- [20] Knapp K., On the bi-stable J-homomorphism, in: Lecture Notes in Math., 763, Springer, 1979, pp. 13-22. Zbl0429.55005MR561211
- [21] Ljusternik L., Schnirelmann L., Methodes topologiques dans les problèmes variationels, Hermann, Paris, 1934. Zbl0011.02803
- [22] Mahowald M., Some Whitehead products in Sn, Topology4 (1965) 17-26. Zbl0142.40704MR178467
- [23] Mahowald M., A new infinite family in 2π∗S, Topology16 (1977) 249-256. Zbl0357.55020
- [24] Mahowald M., Thompson R.D., The EHP sequence and periodic homotopy, in: James I.M. (Ed.), Hanbook of Algebraic Topology, Elsevier, Amsterdam, 1995, pp. 397-423. Zbl0865.55011MR1361895
- [25] Matsumoto T., On the minimal ordered Morse functions, Publ. RIMS Kyoto Univ.14 (1978) 673-684. Zbl0409.57033MR527195
- [26] McGibbon Ch., The Mislin genus of a space, in: CRM Proc. Lecture Notes, 6, American Mathematical Society, 1994, pp. 75-102. Zbl0820.55007MR1290585
- [27] Milnor J., On the cobordism ring Ω∗ and a complex analogue, Amer. J. Math.82 (1960) 505-521. Zbl0095.16702
- [28] Milnor J., Morse Theory, Ann. of Math. Studies, Princeton University Press, 1963. Zbl0108.10401MR163331
- [29] Quillen D.G., The Adams conjecture, Topology10 (1970) 67-80. Zbl0219.55013MR279804
- [30] Roitberg J., Lusternik–Schnirelmann category of some infinite complexes, Topology39 (2000) 95-101. Zbl0933.55004MR1710994
- [31] Schwarz M., Morse Homology, Progress in Mathematics, 111, Birkhauser, 1993. Zbl0806.57020MR1239174
- [32] Sharko V., Functions on Manifolds, Transl. of Math. Monographs, 131, American Mathematical Society, 1993. Zbl0791.57001MR1248167
- [33] Smale S., Differentiable dynamical systems, Bull. Amer. Math. Soc.73 (1967) 747-817. Zbl0202.55202MR228014
- [34] Smith L., Manifolds with few cells and the stable homotopy of spheres, Proc. Amer. Math. Soc.31 (1) (1972) 279-285. Zbl0232.55027MR296957
- [35] Spivak M., Spaces satisfying Poincaré duality, Topology6 (1967) 77-101. Zbl0185.50904MR214071
- [36] Stanley D., Spaces of Lusternik–Schnirelmann category n and of cone-length n+1, Topology39 (2000) 985-1019. Zbl0978.55002MR1763960
- [37] Sullivan D., Genetics of homotopy theory and the Adams conjecture, Ann. of Math.100 (1974) 1-79. Zbl0355.57007MR442930
- [38] Toda H., Composition Methods in the Homotopy Groups of Spheres, Ann. of Math. Studies, 49, Princeton Univ. Press, 1962. Zbl0101.40703MR143217
- [39] Wall C.T.C., Classification problems in differential topology IV, Topology3 (1966) 73-94. Zbl0149.20501MR192509
- [40] Whitehead G., Elements of Homotopy Theory, Grad. Texts in Math., 61, Springer, 1978. Zbl0406.55001MR516508
- [41] Witten E., Supersymmetry and Morse theory, J. Differential Geom.17 (1982) 661-692. Zbl0499.53056MR683171
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