515 research outputs found
Examples of rational toral rank complex
In "A Hosse diagram for rational toral tanks," we see a CW complex , which gives a rational homotopical classification of almost free toral
actions on spaces in the rational homotopy type of associated with rational
toral ranks and also presents certain relations in them. We call it the {\it
rational toral rank complex} of . It represents a variety of toral actions.
In this note, we will give effective 2-dimensional examples of it when is a
finite product of odd spheres. This is a combinatorial approach in rational
homotopy theory.Comment: 8 page
A Lower Bound for the Rational LS-category of a Coformal Elliptic Space
We give a lower bound for the rational LS-category of certain spaces, including the coformal elliptic ones, in terms of the dimension of its total rational cohomology.</p
Rational toral rank of a map
Let and be simply connected CW complexes with finite rational
cohomologies. The rational toral rank of a space is the largest
integer such that the torus can act continuously on a CW-complex in
the rational homotopy type of with all its isotropy subgroups finite
\cite{H}. As a rational homotopical condition to be a toral map preserving
almost free toral actions for a map , we define the rational toral
rank of , which is a natural invariant with for
the identity map of . We will see some properties of it by Sullivan
models, which is a free commutative differential graded algebra over \Q
\cite{FHT}.Comment: 8 page
A Lower Bound for the LS Category of a Formal Elliptic Space
We give a lower bound for the LS category of a formal elliptic space in terms of its rational cohomology.</p
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