This is an announcement for the paper On the Pelczynski conjecture on Auerbach Bases” by Andrzej Weber<http://arxiv.org/find/math/1/au:+Weber_A/0/1/0/all/0/1>, Michał Wojciechowski<http://arxiv.org/find/math/1/au:+Wojciechowski_M/0/1/0/all/0/1>.
Abstract: We consider Auerbach bases in a Banach spaces of dimension $n>2$. We show that there exists at least $(n-1)n/2+1$ such bases. This estimate follows from the calculation of the Lusternik-Schnirelmann category of the flag variety. A better estimate is obtained for generic Banach spaces by the Morse theory.
The paper may be downloaded from the archive by web browser from URL
http://arxiv.org/abs/1608.00495
