Topological applications of graded Frobenius $n$-homomorphisms, II
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D. V. Gugnin
Translated by: A. Martsinkovsky - Trans. Moscow Math. Soc. 2012, 167-182
- DOI: https://doi.org/10.1090/S0077-1554-2013-00201-0
- Published electronically: January 24, 2013
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Abstract:
This paper strengthens Theorems 3.1.7 and 3.2.4 in Topological applications of graded Frobenius n-homomorphisms, by D. V, Gugnin, Tr. Mosk. Mat. Obs. 72 (2011), no. 1, 127–188; English transl., Trans. Moscow Math. Soc. 72 (2011), no. 1, 97–142. The improved version of Theorem 3.1.7 allows us to use integral techniques when working with rational cohomology algebras of $nH$-spaces. We introduce a rather broad class of even-dimensional manifolds $\mathcal {M}$ and, using integrality conditions, we show that those manifolds do not admit a 2-valued multiplication with identity. In particular, we show that complex projective spaces $\mathbb {C}P^m, m\ge 2,$ are not $2H$-spaces. This fact has only been known for $\mathbb {C}P^2$.References
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Bibliographic Information
- D. V. Gugnin
- Affiliation: Chair of Higher Geometry and Topology, Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia
- Email: dmitry-gugnin@yandex.ru
- Published electronically: January 24, 2013
- Additional Notes: Supported by the RFFI grants 11-01-00694-a and 12-01-92104-YaF-a, and the RF Government Grant RF no. 2010-220-01-077, Contract 11.G34.31.0005.
- © Copyright 2013 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2012, 167-182
- MSC (2010): Primary 13A02, 16T05, 55P45, 57N65
- DOI: https://doi.org/10.1090/S0077-1554-2013-00201-0
- MathSciNet review: 3184973