分野別セミナー

A real moment-angle complex (RMAC), being a special polyhedral product determined by a simplicial complex K, is called a real moment-angle manifold (RMAM) if it is a topological manifold. With the assumption that K is a flag complex (i.e. any set of vertices of K that are pairwise connected by edges spans a simplex of K), M. Davis characterized when a RMAC is a RMAM through the combinatorial topology of K. In this talk, with a different approach, it will be illustrated that Davis's characterization theorem holds for general K, and the algebraic topology of RMAMs will also be discussed, with emphasis on the cup and cap products in their (co)homology.