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

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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, 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/}
}
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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/