Algebras over operad of spheres (Q1956591)

In this paper, the author defines an operad structure on multidimensional spheres. This is done through a more general construction on semigroups [\textit{S. N. Tronin} and \textit{O. A. Kopp}, Izv. Vyssh. Uchebn. Zeved, Mat. 2000, No.~6, 53--62 (2000; Zbl 0992.18008)]. The author uses this general framework to define operad structures on spheres, disks, and orthogonal sets of arbitrary dimension. He then analyses the structure of these operads, showing first that higher-dimensional versions of each are isomorphic to one of two lower-dimensional versions, depending on the parity of the dimension. The paper then goes on to analyze the (rational) structure of algebras over the sphere operad. He does this by defining a variety \(M\) explicitly by its relations, and showing that algebras over the sphere operad are rationally equivalent to \(M\).