Certain phase transitions between topological quantum field theories (TQFTs) 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. Furthermore, this includes (as the case k =more »
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