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Topological applications of graded Frobenius $$n$$-homomorphisms. II. (English. Russian original) Zbl 1273.13002
Trans. Mosc. Math. Soc. 2012, 167-182 (2012); translation from Tr. Mosk. Mat. O.-va 73, No. 2, 207-228 (2012).
In the main result of the paper, the authors prove that if $$X$$ is a connected Hausdorff space homotopy equivalent to a CW-complex such that $$\mathrm{dim}H^q (X;\mathbb{Q}) < \infty$$ for all $$q> 0$$ then the algebra $$H^\ast (X;\mathbb{Q})$$ has a structure of graded $$n$$-Hopf prealgebras provided that $$X$$ has a structure of $$nH$$-space, respectively $$H^\ast (X;\mathbb{Q})$$ has a structure of a graded $$n$$-bialgebra if $$X$$ has a structure of a $$nH$$-monoid (Theorem 1). Moreover, if $$X$$ admits a structure of a $$2H$$-space, then its fundamental group $$\pi_1(X)$$ does not belong to the class $$\mathcal{C}$$ (Theorem 2).
##### MSC:
 13A02 Graded rings 16T05 Hopf algebras and their applications 55P45 $$H$$-spaces and duals 57N65 Algebraic topology of manifolds
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##### References:
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