Finite-dimensional categorical complement theorems in strong shape theory and a principle of reversing maps between open subsets of spheres
Mrozik, Peter
Compositio Mathematica, Tome 80 (1991), p. 179-197 / Harvested from Numdam
Publié le : 1991-01-01
@article{CM_1991__77_2_179_0,
     author = {Mrozik, Peter},
     title = {Finite-dimensional categorical complement theorems in strong shape theory and a principle of reversing maps between open subsets of spheres},
     journal = {Compositio Mathematica},
     volume = {80},
     year = {1991},
     pages = {179-197},
     mrnumber = {1091897},
     zbl = {0721.55006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1991__77_2_179_0}
}
Mrozik, Peter. Finite-dimensional categorical complement theorems in strong shape theory and a principle of reversing maps between open subsets of spheres. Compositio Mathematica, Tome 80 (1991) pp. 179-197. http://gdmltest.u-ga.fr/item/CM_1991__77_2_179_0/

1 F.W. Bauer, Some relations between shape constructions, Cahiers Topologie Géom. Diff. 19 (1978), 337-367. | Numdam | MR 515162 | Zbl 0404.54028

2 A. Calder and H.M. Hastings, Realizing strong shape equivalences, J. Pure Appl. Algebra 20 (1981), 129-156. | MR 601680 | Zbl 0457.55004

3 F.W. Cathey, Strong shape theory in: Shape theory and Geometric Topology, (ed. S. Mardešiċ, J. Segal), 215-238 Lecture Notes in Math. 870, Springer, Berlin -Heidelberg-New York 1981. | MR 643532 | Zbl 0473.55011

4 J. Dydak and J. Segal, Strong shape theory, Diss. Math. 192 (1981), 1-42. | MR 627528 | Zbl 0474.55007

5 D.A. Edwards and H.M. Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Math. 542, Springer, Berlin -Heidelberg-New York 1976. | MR 428322 | Zbl 0334.55001

6 Q. Haxhibeqiri and S. Nowak, Stable shape, Lecture given at the Conference on Geometric Topology and Shape Theory, Dubrovnik 1986.

7 Y. Kodama and J. Ono, On fine shape theory, Fund. Math. 105 (1979), 29-39. | MR 558127 | Zbl 0425.54016

8 Yu. T. Lisica, On the exactness of the spectral homotopy group sequence in shape theory, Soviet Math. Dok. 18 (1977), 1186-1190. | Zbl 0398.55012

9 Yu. T. Lisica and S. Mardešić, Coherent prohomotopy theory and strong shape of metric compacta, Glasnik Mat. 20 (40) (1985), 159-186. | MR 818622 | Zbl 0592.55007

10 S Mardešić and J. Segal, Shape Theory, North-Holland, Amsterdam 1982. | MR 676973 | Zbl 0495.55001

11 P. Mrozik, Hereditary shape equivalences and complement theorems, Topology Appl. 22 (1986), 131-137. | MR 836320 | Zbl 0598.54006

12 P. Mrozik, Chapman's category isomorphism for arbitrary ARs, Fund. Math. 125 (1985), 195-208. | MR 813757 | Zbl 0592.57013

13 P. Mrozik, Finite-dimensional categorical complement theorems in shape theory, Compositio Math. 68 (1988), 161-173. | Numdam | MR 966578 | Zbl 0665.55006

14 S. Nowak, On the relationship between shape properties of subcompacta of Sn and homotopy properties of their complements, Fund. Math. 128 (1987), 47- 59. | MR 919289 | Zbl 0633.55009

15 D. Quillen, Homotopical Algebra, Lecture Notes in Math. 43, Springer, Berlin -Heidelberg-New York 1967. | MR 223432 | Zbl 0168.20903

16 R.B. Sher, Complement theorems in shape theory, in: Shape Theory and Geometric Topology (ed. S. Mardešić, J. Segal), 150-168, Lecture Notes in Math. 870, Springer, Berlin-Heidelberg-New York 1981. | MR 643529 | Zbl 0494.57007

17 R.B. Sher, Complement theorems in shape theory II, in: Geometric Topology and Shape Theory (ed. S. Mardešić, J. Segal), 212-220, Lecture Notes in Math. 1283, Springer, Berlin-Heidelberg -New York 1987. | MR 922283 | Zbl 0631.55006

18 E.H. Spanier, Algebraic Topology, McGraw-Hill, New York 1966. | MR 210112 | Zbl 0145.43303

19 R.M. Switzer, Algebraic Topology-Homotopy and Homology, Springer, Berlin 1975. | MR 385836 | Zbl 1003.55002

20 G.A. Venema, Embeddings of compacta in the trivial range, Proc. Amer. Math. Soc. 55 (1976), 443-448. | MR 397738 | Zbl 0332.57005