On page 2 of the paper "2 + 1 dimensional gravity as an exactly soluble system" Witten claims that:
Depending on its topology, a finite-dimensional phase space might be unquantizable,
How a classical phase space might be unquantizable? Is it special to finite dimensional phase space or some infinite dimensional phase spaces also might be unquantizable? What are sufficient and necessary conditions quantizability of a classical phase space?
Is not it a problem for quantum mechanics which some classical system have not quantum counterpart?