Construction of compact constant mean curvature hypersurfaces with topology (Q442127)

In the paper under review the author uses the end-to-end gluing of constant mean curvature surface developed by \textit{J. Ratzkin} in his PhD thesis [``An end-to-end construction of constant mean curvature'', Univ. Washington (2001)] and the moduli space theory investigated by \textit{R. Kusner}, \textit{R. Mazzeo} and \textit{D. Pollack} [Geom. Funct. Anal. 6, No. 1, 120--137 (1996; Zbl 0966.58005)] to produce compact constant mean curvature hypersurfaces with nontrivial topology. To simplify reasonings the author assumes that considered hypersurfaces have a large group of symmetry but his method can be obviously used to give surfaces with less symmetries.