Geodesic
Lefschetz Numbers for Maps of Fiber Spaces
Matematičeskie zametki, Tome 84 (2008) no. 5, pp. 643-657 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : Poincaré duality. 
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     author = {D. V. Artamonov},
     title = {Lefschetz {Numbers} for {Maps} of {Fiber} {Spaces}},
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     year = {2008},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a0/}
}
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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