  Certain phase transitions between topological quantum field theories (TQFT)
are driven by the condensation of bosonic anyons. However, as bosons in a TQFT
are themselves nontrivial collective excitations, there can be topological
obstructions that prevent them from condensing. Here we formulate such an
obstruction in the form of a no-go theorem. We use it to show that no
condensation is possible in SO(3)$_k$ TQFTs with odd $k$. We further show that
a layered theory obtained by tensoring SO(3)$_k$ TQFT with itself any integer
number of times does not admit condensation transitions either. This includes
(as the case $k=3$) the noncondensability of any number of layers of the
Fibonacci TQFT.
