Is there a Lie group G which has only two cells?

i.e. $ G = S^n \cup_f~ e^m$ where $f:S^{m-1}\to S^n$ with $m>n$

How many exists that groups? Infinitely many?

Is there a Lie group G which has only two cells?

i.e. $ G = S^n \cup_f~ e^m$ where $f:S^{m-1}\to S^n$ with $m>n$

How many exists that groups? Infinitely many?

If there is no Lie group which has only two cell, how many cells needed to a Lie group?