CHARACTERIZATION OF THE MOD 3 COHOMOLOGY OF THE COMPACT, CONNECTED, SIMPLE, EXCEPTIONAL LIE GROUPS OF RANK 6.

It is shown that the mod $3$ cohomology of a $1$</formtex>-connected, homotopy associative mod $3$</formtex> $H$</formtex>-space that is rationally equivalent to the Lie group $E_6$</formtex> is isomorphic to that of $E_6$</formtex> as an algebra. Moreover, it is shown that the mod $3$</formtex> cohomology of a nilpotent, homotopy-associative mod $3$</formtex> $H$</formtex>-space that is rationally equivalent to $E_6$</formtex>, and whose fundamental group localized at $3$</formtex> is non-trivial, is isomorphic to that of the Lie group $\Ad E_6$</formtex> as a Hopf algebra over the mod $3$</formtex> Steenrod algebra. It is also shown that the mod $3$</formtex> cohomology of the universal cover of such an $H$</formtex>-space is isomorphic to that of $E_6$</formtex> as a Hopf algebra over the mod $3$</formtex> Steenrod algebra. [ABSTRACT FROM AUTHOR]