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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 867247, 8 pages
Research Article

Examples of Rational Toral Rank Complex

Faculty of Education, Kochi University, 2-5-1 Akebono-Cho, Kochi 780-8520, Japan

Received 21 December 2011; Accepted 6 March 2012

Academic Editor: Frank Werner

Copyright © 2012 Toshihiro Yamaguchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.