  The existence of electronic symmetry breaking in the underdoped cuprates, and
its disappearance with increased hole-density $p$, are now widely reported.
However, the relationship between this transition and the momentum space
($\vec{k}$-space) electronic structure underpinning the superconductivity has
not been established. Here we visualize the $\vec{Q}$=0 (intra-unit-cell) and
$\vec{Q}\neq$0 (density wave) broken-symmetry states simultaneously with the
coherent $\vec{k}$-space topology, for Bi$_2$Sr$_2$CaCu$_2$O$_{8+d}$ samples
spanning the phase diagram 0.06$\leq p \leq$0.23. We show that the electronic
symmetry breaking tendencies weaken with increasing $p$ and disappear close to
$p_c$=0.19. Concomitantly, the coherent $\vec{k}$-space topology undergoes an
abrupt transition, from arcs to closed contours, at the same $p_c$. These data
reveal that the $\vec{k}$-space topology transformation in cuprates is linked
intimately with the disappearance of the electronic symmetry breaking at a
concealed critical point.
