Real spin bordism and orientations of topological $\mathrm{K}$-theory

Zachary Halladay, Yigal Kamel

We construct a commutative orthogonal $C_2$-ring spectrum, ${\mathrm{MSpin}}_{\mathbb{R}}^c$, along with a $C_2$-$E_{\infty }$-orientation $\mathrm{MSpin}^c_{\mathbb{R}} \to \mathrm{K…