... > topology > algebraic topology > manifold > differentiable manifold > Lie group > real form

... > geometry > topological space > manifold > differentiable manifold > Lie group > real form

geometry > differential geometry > differentiable manifold > Lie group > real form

topology > differential topology > differentiable manifold > Lie group > real form

algebra > group theory > topological group > Lie group > real form

algebra > differential algebra > Lie algebra > real form

... > algebra > abstract algebra > algebraic structure > algebra over a field > Lie algebra > real form