Geodesic
Normal fibrations of polyhedra, and duality
Sbornik. Mathematics, Tome 50 (1985) no. 1, pp. 177-189 
V. E. Kolosov. Normal fibrations of polyhedra, and duality. Sbornik. Mathematics, Tome 50 (1985) no. 1, pp. 177-189. http://geodesic.mathdoc.fr/item/SM_1985_50_1_a11/
@article{SM_1985_50_1_a11,
     author = {V. E. Kolosov},
     title = {Normal fibrations of polyhedra, and duality},
     journal = {Sbornik. Mathematics},
     pages = {177--189},
     year = {1985},
     volume = {50},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_50_1_a11/}
}
TY  - JOUR
AU  - V. E. Kolosov
TI  - Normal fibrations of polyhedra, and duality
JO  - Sbornik. Mathematics
PY  - 1985
SP  - 177
EP  - 189
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1985_50_1_a11/
LA  - en
ID  - SM_1985_50_1_a11
ER  - 
%0 Journal Article
%A V. E. Kolosov
%T Normal fibrations of polyhedra, and duality
%J Sbornik. Mathematics
%D 1985
%P 177-189
%V 50
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1985_50_1_a11/
%G en
%F SM_1985_50_1_a11

Voir la notice de l'article provenant de la source Math-Net.Ru

A duality theory is constructed in the category of stable finite fibrations over a finite polyhedron $X$. With the aid of this theory, a result is obtained about the stable characterization of the normal fibration of the polyhedron, in the class of finite reducible fibrations over $X$. As a corollary, the uniqueness theorem is proved for $\Lambda$-Spivak fibrations over $\Lambda$-Poincaré complexes, for an arbitrary commutative ring $\Lambda$. Also, a result is obtained concerning the space of stable self-equivalences of the fiber of the normal fibration of $X$. Bibliography: 10 titles.

[1] Browder W., Surgery on the simply connected manifolds, Springer-Verlag, 1972 | MR

[2] Rurk K., Sanderson B., Vvedenie v kusochno-lineinuyu topologiyu, Mir, M., 1974 | MR

[3] Spivak M., “Spaces, satisfying Poincare duality”, Topology, 6 (1967), 77–101 | DOI | MR | Zbl

[4] Browder W., “Poincare spaces, their normal bundles and surgery”, Inv. math., 17 (1972), 191–202 | DOI | MR | Zbl

[5] Levitt N., “Normal fibrations for complexes”, Ill. J. Math., 14 (1970), 385–408 | MR | Zbl

[6] Spanier E., “Function spaces and duality”, Ann. Math., 70 (1959), 338–378 | DOI | MR | Zbl

[7] Spanier E., Whitehead J. H. C., “Duality in homotopy theory”, Mathematica, 2 (1955), 56–80 | MR | Zbl

[8] Bold A., Puppe D., Duality, trace and transfer (Proc. Inter. Conference on Geometric topology), Polish Scientific Publisher, Warszawa, 1978

[9] Wall C. T. C., “Thickening”, Topology, 5 (1966), 73–94 | DOI | MR | Zbl

[10] Mosher R., “Note on the generalized Whitney sum”, Proc. A. M. S., 20 (1969), 383–384 | DOI | MR | Zbl