We show how a suitably twisted spin cobordism spectrum connects to the question of existence of metrics of positive scalar curvature on closed, smooth manifolds by building on fundamental work of Gromov, Lawson, Rosenberg, Stolz and others. We then investigate this parametrised spectrum, compute its $mod2$‐cohomology and generalise the Anderson–Brown–Peterson splitting of the usual spin cobordism spectrum to the twisted case. Along the way we also describe the $mod2$‐cohomology of various twisted, connective covers of real $K$‐theory. In an Appendix we provide a comparison of our geometric models of twisted spin cobordism and twisted $K$‐theory with others arising from abstract homotopy theory.

中文翻译：

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扭曲自旋共轴主义和标量正曲率

我们展示了如何根据Gromov，Lawson，Rosenberg，Stolz等人的基础工作，将适当扭曲的自旋cobordism谱图与封闭，光滑流形上正标量曲率度量的存在联系起来。然后，我们研究此参数化频谱，计算其$米Ød2$-同调，并将通常的自旋共轴主义谱的安德森-布朗-彼得森分裂分解为扭曲的情况。一路上我们还描述了$米Ød2$-各种扭曲，结实的覆盖物的同调 $ķ$-理论。在附录中，我们比较了扭曲的自旋共轴性和扭曲的几何模型$ķ$-与抽象同伦理论相关的理论。