Is there a comprehensive account of GEOMETRIC equivariant spin bordism groups with respect to the group $ \mathbb{Z}/2$ (instead of homotopy theoretical trough equivariant Thom Spectra), which allow actions which are not free?. I am interested only in low dimensions 0 to 6.
There is a computation of the free bordism groups done by Gianvalbo (1976, conference proceedings of transformation groups conference in newcastle upon Tyne), Using KO Pontrjagyn classes and the splitting method from Anderson-Brown-Peterson to determine the free bordism groups by making the trick of computing $\Omega_n^{\rm Spin}(B \mathbb{Z}/2)$. However, this computation is seriously flawed, producing groups with a higher rank as possible, as one can easily check with the Atiyah-Hirzebruch Spectral sequence.
