From the literature I learned that the Pin$^-$ bordism group of a point in 10 dimensions is:
$$\Omega_{10}^{Pin^-}(pt)=\mathbb{Z}_{128} \times \mathbb{Z}_{8} \times \mathbb{Z}_{2}$$
What are their 10-dimension manifold generators?
What are their topological invariants (characteristic classes, or manifold signatures, or Dirac operators, eta or ABK invariants) can distinguish all $\mathbb{Z}_{128} \times \mathbb{Z}_{8} \times \mathbb{Z}_{2}$ classes?