Examples of rational toral rank complex

Details Examples of rational toral rank complex Examples of rational toral rank complex

2012-03-20

arxiv.org/abs/1203.4317v1

Mathematics

Algebraic Topology

8 pages

Scientific paper

In "A Hosse diagram for rational toral tanks," we see a CW complex ${\mathcal T}(X)$, 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 {\it 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.

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