I recently developed a non-linear $\sigma$ model approach ( http://arxiv.org/abs/1410.8477 ) to address this issue.
Let $\text{iTO}_L^n$ be the set of the *fully extended* TQFTs in $n$-dimensions, that assign a 1-dimensional vector space to every compact oriented $(n−1)$-manifold. (Physically, $\text{iTO}_L^n$ is the set of L-type
topologically-ordered phases in $n$-dimensional space-time that have no
topological excitations.) Such a set, $\text{iTO}_L^n$, actually from an Abelain group.

We find that
$\text{iTO}_L^1=\text{iTO}_L^2=\text{iTO}_L^4=\text{iTO}_L^6=0$,
$\text{iTO}_L^3=\mathbb{Z}$, $\text{iTO}_L^5=\mathbb{Z}_2$,
$\text{iTO}_L^7=2\mathbb{Z}$.

Here $\text{iTO}_L^3=\mathbb{Z}$ is generated by $\omega_3$ with d$\omega_3=p_1$ and $p_1$ the first Pontryagin class.

Similar results are also obtained in
http://arxiv.org/abs/1403.1467 using cobordism approach. But we disagree on the generators of $\text{iTO}_L^3=\mathbb{Z}$ and $\text{iTO}_L^7=2\mathbb{Z}$. For example,
in http://arxiv.org/abs/1403.1467 , the generator of $\text{iTO}_L^3=\mathbb{Z}$
is $\frac13 \omega_3$ instead of $\omega_3$.

In http://arxiv.org/abs/1406.7278 , the generator of $\text{iTO}_L^3=\mathbb{Z}$
is $\frac16 \omega_3$, instead of $\omega_3$ or $\frac13 \omega_3$.