Examples of Rational Toral Rank Complex - Toshihiro Yamaguchi (International Journal of Mathematics and Mathematical Sciences)
There is a CW complex 𝒯(𝑋), which gives a rational homotopical classification of almost free toral actions on spaces in the rational homotopy type of X associated with rational toral ranks and also presents certain relations in them. We call it the rational toral rank complex of X. It represents a variety of toral actions. In this note, we will give effective 2-dimensional examples of it when X is a finite product of odd spheres. This is a combinatorial approach in rational homotopy theory.