For any oriented cusped hyperbolic 3-manifold $M$$M$, we study its $(R,\epsilon )$$(R,\epsilon )$-panted cobordism group, which is the abelian group generated by $(R,\epsilon )$$(R,\epsilon )$-good curves in $M$$M$ modulo the oriented boundaries of $(R,\epsilon )$$(R,\epsilon )$-good pants. In particular, we prove that for sufficiently small $\epsilon >0$$\epsilon >0$ and sufficiently large $R>0$$R>0$, some modified version of the $(R,\epsilon )$$(R,\epsilon )$-panted cobordism group of $M$$M$ is isomorphic to $H_1(\text{SO}(M);\mathbb{Z})$$H_1(\text{SO}(M);\mathbb{Z})$.

中文翻译：

---

尖瓣双曲 3 流形的喘息共边群

对于任何定向尖顶双曲 3 流形$米$$M$, 我们研究它$(R,\epsilon )$$(R,\epsilon )$-panted cobordism group，这是由$(R,\epsilon )$$(R,\epsilon )$- 良好的曲线$米$$M$模的定向边界$(R,\epsilon )$$(R,\epsilon )$- 好裤子。特别是，我们证明对于足够小的$\epsilon >0$$\epsilon >0$并且足够大$R>0$$R>0$, 的一些修改版本$(R,\epsilon )$$(R,\epsilon )$-气喘吁吁的协调组$米$$M$同构于$H_1(\text{所以}(米);\mathbb{Z})$$H_1(\text{SO}(M);\mathbb{Z})$.