Geodesic
Exotic invariant for 6-manifolds: a~direct construction
Algebra i analiz, Tome 21 (2009) no. 3, pp. 145-164.

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Some of the author's previous works, dealing with the classification problem for simply connected closed 6-manifolds, contain a construction of a certain “exotic” invariant $\Gamma$. This construction is substantially indirect and based on nontrivial calculations. In the present paper, a direct construction is suggested, which does not depend on the calculations mentioned and involves only some simple surgery, plus some well-known identities for Stiefel-Whitney and Pontryagin classes, namely, “modulo 2” and “modulo 4” Wu formulas. 
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A. V. Zhubr. Exotic invariant for 6-manifolds: a~direct construction. Algebra i analiz, Tome 21 (2009) no. 3, pp. 145-164. http://geodesic.mathdoc.fr/item/AA_2009_21_3_a5/

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