A suspension theorem for the proper homotopy and strong shape theories
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume 36 (1995) no. 2, p. 98-126
@article{CTGDC_1995__36_2_98_0,
     author = {Elvira-Donazar, C. and Hernandez-Paricio, L. J.},
     title = {A suspension theorem for the proper homotopy and strong shape theories},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {36},
     number = {2},
     year = {1995},
     pages = {98-126},
     zbl = {0837.55007},
     mrnumber = {1338466},
     language = {en},
     url = {http://www.numdam.org/item/CTGDC_1995__36_2_98_0}
}
Elvira-Donazar, C.; Hernandez-Paricio, L. J. A suspension theorem for the proper homotopy and strong shape theories. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume 36 (1995) no. 2, pp. 98-126. http://www.numdam.org/item/CTGDC_1995__36_2_98_0/

[1] A. Artin and B. Mazur, "Étale Homotopy", Lect. Notes in Math., n 100, Springer, 1969. | MR 245577 | Zbl 0182.26001

[2] H.J. Baues, "Algebraic homotopy", Cambridge Univ. Press, 1988. | MR 985099 | Zbl 0688.55001

[3] H.J. Baues, "Foundations of proper homotopy theory", preprint 1992.

[4] A.K. Bousfield and D.M. Kan, "Homotopy limits, Completions and Localizations ", Lecture Notes in Maths. 304, Springer-Verlag,1972. | MR 365573 | Zbl 0259.55004

[5] K. Borsuk, "Concerning homotopy properties of compacta ", Fund. Math. 62 (1968) 223-254. | MR 229237 | Zbl 0159.24603

[6] E.M. Brown, "On the proper homotopy type of simplicial complexes" Lect. Notes in Math., n 375 (1975).

[7] J. Cabeza, M.C. Elvira and L.J. Hernindez, "Una categoría cofibrada para las aplicaciones propias", Actas del las XIV Jorn. Mat. Hispano-Lusas., sección Geometria y Topologia (1989), Univ. de La Laguna.

[8] Z. Cerin, "On various relative proper homotopy groups", Tsukuba J. Math., vol 4, 2 (1980) 177-202. | MR 623435 | Zbl 0469.55011

[9] J.M. Cordier and T. Porter, "Shape Theory. Categorical methods of approximation", Ellis Horwood Series in Math. and its Appl., 1989. | MR 1000348 | Zbl 0663.18001

[10] D. Edwards and H. Hastings, "Čech and Steenrod homotopy theories with applications to Geometric Topology", Lect. Notes Math., 542, Springer, 1976. | MR 428322 | Zbl 0334.55001

[11] C. Elvira, "Aplicaciones propias de X en Rn+1", Actas del IV Sem. de Topologia, Bilbao (1988).

[12] H. Freudenthal, "Über die Klassen der Sphärenabbildungen", Compositio Math., 5 (1937) 299-314. | JFM 63.1161.02 | Numdam

[13] P. Gabriel and M. Zisman, "Calculus of fractions and homotopy theory", Springer, Berlin (1966). | MR 210125 | Zbl 0186.56802

[14] J.W. Grossman, "A homotopy theory of pro-spaces", Trans. Amer. Math. Soc., 201 (1975) 161-176. | MR 356039 | Zbl 0266.55007

[15] J.W. Grossman, "Homotopy classes of maps between pro-spaces ", Michigan Math. J. 21 (1974) 355-362. | MR 367984 | Zbl 0293.55005

[16] J.W. Grossman, "Homotopy groups of Pro-spaces", Illinois J. Math. 20 (1976) 622-625. | MR 413097 | Zbl 0329.55011

[17] A. Grothendieck, "Technique De Descente Et Théorèmes d'Existence En Géométrie Algèbrique I-IV", Seminar Bourbaki, Exp. 190, 195, 212, 221, 1959-60, 1960-61. | Numdam | Zbl 0229.14007

[18] J.D.P. Meldrum, "Near-rings and their links with groups", Pitman Publishing Inc, 1985. | MR 854275 | Zbl 0658.16029

[19] S. Mardešié and J. Segal, "Shape theory", North-Holland, 1982. | MR 676973 | Zbl 0495.55001

[20] T. Porter, "Cech Homotopy I", J. London Math. Soc. 90 (1974) 8-26. | MR 321080 | Zbl 0254.55012

[21] T. Porter, "Stability Results for Topological spaces", Math. Z. 140 (1974) 1-21. | MR 385846 | Zbl 0275.55022

[22] T. Porter, "Abstract homotopy theory in procategories", Cahiers de topologie et geometrie differentielle, vol 17 (1976) 113-124. | Numdam | MR 445496 | Zbl 0349.18012

[23] T. Porter, "Coherent prohomotopical algebra", Cahiers de topologie et geometrie differentielle", vol 18 (1977) 139-179. | Numdam | MR 470033 | Zbl 0364.18009

[24] T. Porter, "Coherent pro-homotopy theory", Cahiers de topologie et geometrie differentielle", vol 19 n 1 (1978) 3-45. | Numdam | MR 496541 | Zbl 0387.55013

[25] T. Porter, "Čech and Steenrod homotopy and the Quigley exact couple in strong shape and proper homotopy Theory", J. Pure Apl. Alg. 24 (1983) 303-312. | MR 656853 | Zbl 0485.55009

[26] T. Porter, "Homotopy groups for strong shape and proper homotopy", Convegnio di Topologia serie II n 4 (1984) 101-113. | MR 769857 | Zbl 0568.55009

[27] T. Porter, "Proper homotopy, prohomotopy and coherence ", U.C.N.W. Pure Maths Preprint 86.20.

[28] T. Porter, "On the two definitions of Ho(proC)", Top. and its Appl. 28 (1988) 289-293. | MR 931529 | Zbl 0647.18008

[29] D. Quillen, "Homotopical Algebra", Lect. Notes in Math, 43, Springer, 1967. | MR 223432 | Zbl 0168.20903

[30] J.B. Quigley, "An exact sequence from the nth to the (n-1)-st fundamental group", Fund. Math. 77 (1973) 195-210. | MR 331379 | Zbl 0247.55010

[31] E. Spanier, "Borsuk's cohomotopy groups", Ann. of Math., 50 (1949) 203-245. | MR 29170 | Zbl 0032.12402

[32] N.E. Steenrod, "Regular Cycles on Compact Metric Spaces", Ann. of Math. 41 (1940) 833-851. | MR 2544 | Zbl 0025.23405

[33] Strøm, " The homotopy category is a homotopy category", Arch. Math. 23 (1973) 435-441. | MR 321082 | Zbl 0261.18015