Geodesic
Lefschetz Numbers for Maps of Fiber Spaces
Matematičeskie zametki, Tome 84 (2008) no. 5, pp. 643-657.

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

Expressions for the Lefschetz numbers of maps of fiber spaces in terms of those of maps of the fibers and the base are obtained. A similar problem is considered for Lefschetz coincidence numbers.
Keywords: Lefschetz number, map of fiber spaces, Euler characteristic, Leray sheaf, Lefschetz coincidence number, spectral sequence, CW-complex, Poincaré duality. 
@article{MZM_2008_84_5_a0,
     author = {D. V. Artamonov},
     title = {Lefschetz {Numbers} for {Maps} of {Fiber} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--657},
     publisher = {mathdoc},
     volume = {84},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a0/}
}
TY  - JOUR
AU  - D. V. Artamonov
TI  - Lefschetz Numbers for Maps of Fiber Spaces
JO  - Matematičeskie zametki
PY  - 2008
SP  - 643
EP  - 657
VL  - 84
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a0/
LA  - ru
ID  - MZM_2008_84_5_a0
ER  - 
%0 Journal Article
%A D. V. Artamonov
%T Lefschetz Numbers for Maps of Fiber Spaces
%J Matematičeskie zametki
%D 2008
%P 643-657
%V 84
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a0/
%G ru
%F MZM_2008_84_5_a0
D. V. Artamonov. Lefschetz Numbers for Maps of Fiber Spaces. Matematičeskie zametki, Tome 84 (2008) no. 5, pp. 643-657. http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a0/

[1] J. Leray, “L'homologie d'un espace fibré dont la fibre est connexe”, J. Math. Pures Appl. (9), 29 (1950), 169–213 | MR | Zbl

[2] J. P. Serre, “Homologie singulière des espace fibrés. Applications”, Ann. of Math. (2), 54 (1951), 425–505 | DOI | MR | Zbl

[3] A. Douady, “Application de la suite spectrale des espace fibrés”, Séminaire Henri Cartan, 11:1 (1958/59), 11 p., Exp. 3; http://www.numdam.org/item?id=SHC_1958-1959__11_1_A3_0

[4] R. Bott, L. V. Tu, Differentsialnye formy v algebraicheskoi topologii, Nauka, M., 1988 | MR | Zbl

[5] D. F. Snyder, “Lefshetz number for sheaf-trivial proper surjections”, Topology Appl., 128:2–3 (2003), 239–246 | DOI | MR | Zbl

[6] G. Bredon, Teoriya puchkov, Nauka, M., 1988 | MR | Zbl

[7] R. Godeman, Algebraicheskaya topologiya i teoriya puchkov, IL, M., 1961 | MR | Zbl

[8] S. Maklein, Gomologiya, Mir, M., 1966 | MR | Zbl