Nothing. It's connected by a few centimeters.
Transverse fissue
You have the beautiful partition called as falx cerebri, which separates the cerebral hemisphere incompletely. This partition is made from the folding of the inner layer of the Dura mater. Dura mater is the outer covering of the meninges.
The cerebellum and cerebral hemispheres
Frontal Parietal Occipital Temporal Cerebellum
The cerebral hemispheres are connected by the corpus callosum.
There is one major fissure that divides the cerebral hemispheres, called the longitudinal fissure. It separates the left and right hemispheres of the brain.
The corpus collasum.
it separates the cerebrum into left and right hemispheres.
amygdala, cerebral cortex and one other im unaware of
medulla oblanga
corrus collasum
The falx cerebri separates the right and left hemispheres.
The falx cerebelli invaginates into the cerebellar notch between the two cerebellar hemispheres. It doesn't actually separate the two hemispheres though. The falx cerebri separates the two cerebral hemispheres.