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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

An exotic invariant for 6-manifolds: The direct construction


Author: A. V. Zhubr
Translated by: the author
Original publication: Algebra i Analiz, tom 21 (2009), nomer 3.
Journal: St. Petersburg Math. J. 21 (2010), 469-482
MSC (2000): Primary 57N15, 57R55
Published electronically: March 1, 2010
MathSciNet review: 2588766
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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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Additional Information

A. V. Zhubr
Affiliation: Mathematics Department, Komi Scientific Center, Urals Division, Russian Academy of Sciences, Chernova Street 3a, Syktyvkar 167998, Russia
Email: a-v-zhubr@yandex.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-10-01104-0
PII: S 1061-0022(10)01104-0
Keywords: 6-manifold, classification, surgery, direct construction, invariant
Received by editor(s): May 20, 2008
Published electronically: March 1, 2010
Additional Notes: This work is partially supported by the program “Problems in non-linear dynamics” of the Presidium of Russian Academy of Sciences
Article copyright: © Copyright 2010 American Mathematical Society