On the cellular decomposition and the Lusternik-Schnirelmann category of   $Spin(7)$
  We give a cellular decomposition of the compact connected Lie group $Spin(7)$. We also determine the L-S categories of $Spin(7)$ and $Spin(8)$. 
Norio Iwase, Mamoru Mimura and Tetsu Nishimoto