Geodesic
Conformity theorems in multiplicative pairs
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 15, Tome 343 (2007), pp. 233-247

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It is proved that two conditions of orientation conformity in multiplicative pairs are equivalent and established conformity of trace homomorphism and Poincare duality. 
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     author = {A. A. Solynin},
     title = {Conformity theorems in multiplicative pairs},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a9/}
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A. A. Solynin. Conformity theorems in multiplicative pairs. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 15, Tome 343 (2007), pp. 233-247. http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a9/