Examples of Rational Toral Rank Complex

Abstract EN

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.