Title of Paper: Two lower bounds for the relative L.S. category.
Author: Pierre-Marie MOYAUX.
AMS Classification numbers:55M30, 57R70.
Addresse of the author: Pierre-Marie MOYAUX;
Universite de Lille 1;
U.F.R. de Mathematiques & U.R.A 751 au CNRS;
59655 Villeneuve D'Ascq, France.
Email address of the author: moyaux@gat.univ-lille1.fr
Included EPS or PS files : none.
Text of Abstract: We prove that
$ \sigma ^{p+1}cat(X) +1 \leq cat(X,X \times S^{p}) $ and that
$e(X,X\times S^{p})=e(X)+1$, where $ \sigma ^{p+1}cat$ is
the $ \sigma-$category of Vandembroucq and $e$ is
the Toomer invariant. The proof is based on an extension to a
relative setting of Milnor's construction of the classifying space
of a topological group.