Geodesic
Topological applications of graded Frobenius $n$-homomorphisms
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 72 (2011) no. 1, pp. 127-188

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This paper generalizes the theory of Frobenius $n$-homomorphisms, as expounded by V. M. Buchstaber and E. G. Rees, to graded algebras, and applies the new algebraic technique of graded Frobenius $n$-homomorphisms to two topological problems. The first problem is to find estimates on the cohomological length of the base and of the total space of a wide class of branched coverings of topological spaces, called the Smith-Dold branched coverings. This class of branched coverings contains, in particular, unbranched finite-sheeted coverings and the usual finite-sheeted branched coverings from the theory of smooth manifolds. The second problem concerns a description of cohomology and fundamental groups of $n$-valued topological groups. The main tool there is a generalization of the notion of a graded Hopf algebra, based on the notion of a graded Frobenius $n$-homomorphism. 
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     author = {D. V. Gugnin},
     title = {Topological applications of graded {Frobenius} $n$-homomorphisms},
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D. V. Gugnin. Topological applications of graded Frobenius $n$-homomorphisms. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 72 (2011) no. 1, pp. 127-188. http://geodesic.mathdoc.fr/item/MMO_2011_72_1_a4/