The homotopy category of the bordism category $h{\mathcal{C}}_d$ has as objects closed oriented $(d-1)$‐manifolds and as morphisms diffeomorphism classes of $d$‐dimensional bordisms. Using a new fiber sequence for bordism categories, we compute the classifying space of $h{\mathcal{C}}_d$ for $d=1$, exhibiting it as a circle bundle over ${\mathrm{\Omega }}^{\infty -2}{\mathbb{CP}}_{-1}^{\infty }$.

中文翻译：

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一维bordism类别的分类空间和空间TC的cobordism模型

Bordism类别的同伦类别 $H{\mathcal{C}}_d$ 作为对象已关闭 $（d-\mathrm{1个}）$的流形和作为微射态的 $d$维度的过时主义。使用针对bordism类别的新纤维序列，我们可以计算出$H{\mathcal{C}}_d$ 对于 $d=\mathrm{1个}$，将其展示为圆形束 ${\mathrm{\Omega }}^{\infty -2}{\mathbb{CP}}_{-\mathrm{1个}}^{\infty }$。