  We use the topological quantum field theory description of states in
Chern-Simons theory to discuss the relation between spacetime connectivity and
entanglement, exploring the paradigm entanglement=topology. We define a special
class of states in Chern-Simons with properties similar to those of holographic
states. While the holographic states are dual to classical geometries, these
connectome states represent classical topologies, which satisfy a discrete
analog of the Ryu-Takayanagi formula and characteristic inequalities for the
entanglement entropy. Generic states are linear combinations of connectomes,
and the theory also has nonperturbative states which are global spacetime
defects formed by a large number of quantum fluctuations. Topological
presentation of quantum states and emergence of topology from entanglement may
be useful for building a generalization to geomentry, that is quantum gravity.
Thinking of further quantum gravity comparisons we discuss replica wormholes
and conclude that similar objects exist beyond gravitational theories. The
topological theory perspective suggests that the sum over all wormholes is
always factorizable, even though the individual ones might not be.
