Geodesic
The signature theorem and some related questions
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 8, Tome 231 (1995), pp. 197-209 
N. Yu. Netsvetaev. The signature theorem and some related questions. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 8, Tome 231 (1995), pp. 197-209. http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a12/
@article{ZNSL_1995_231_a12,
     author = {N. Yu. Netsvetaev},
     title = {The signature theorem and some related questions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {197--209},
     year = {1995},
     volume = {231},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a12/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Some corollaries of the Hirzebruch–Thom signature theorem are discussed. The multiplicativity of the signature and the naturalness of the Pontryagin classes for coverings in the case of $\mathbb Q$-homology manifolds is proved. A geometric proof of Hirzebruch's well-known “functional equation” for the virtual signature is outlined. Bibl. 24 titles.