Geodesic
Characteristic numbers in $U$-theory
Izvestiya. Mathematics , Tome 5 (1971) no. 6, pp. 1365-1385

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We compute the subgroup of $\Omega_*^U\otimes Q$ consisting of all elements with integral $U$-numbers. Using these results, we obtain a new computation of the group $\mathrm{Ext}^1_{A^U}(\Omega_*^U,\Omega_*^U)$ and a complete answer to the question of Chern numbers of $(U,\mathrm{fr})$-manifolds. 
@article{IM2_1971_5_6_a8,
     author = {N. V. Panov},
     title = {Characteristic numbers in $U$-theory},
     journal = {Izvestiya. Mathematics },
     pages = {1365--1385},
     publisher = {mathdoc},
     volume = {5},
     number = {6},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a8/}
}
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N. V. Panov. Characteristic numbers in $U$-theory. Izvestiya. Mathematics , Tome 5 (1971) no. 6, pp. 1365-1385. http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a8/