An exotic invariant for 6-manifolds: The direct construction

Zhubr, A.

doi:10.1090/S1061-0022-10-01104-0

An exotic invariant for 6-manifolds: The direct construction
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by A. V. Zhubr
Translated by: the author

St. Petersburg Math. J. 21 (2010), 469-482

DOI: https://doi.org/10.1090/S1061-0022-10-01104-0

Published electronically: March 1, 2010

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Abstract:

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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