On the Lusternik-Schnirelmann category of spaces with 2-dimensional fundamental group
Abstract
Description
The following inequality
\cat X\le \cat Y+\lceil\frac{hd(X)-r}{r+1}\rceil
holds for every locally trivial fibration between $ANE$ spaces $f:X\to Y$ which admits a section and has the $r$-connected fiber where $hd(X)$ is the homotopical dimension of $X$. We apply this inequality to prove that
\cat X\le \lceil\frac{\dim X-1}{2}\rceil+cd(π_1(X))
for every complex $X$ with $cd(π_1(X))\le 2$.
8 pages
8 pages