Griffiths双锥群同构于三锥群
The Griffiths double cone group is isomorphic to the triple
AI总结：
该研究证明Griffiths双锥空间基本群与三锥及满足基数条件的多锥空间基本群同构，同构非构造且无法由连续映射实现，同时证实了关于其与调和群岛基本群同构的猜想。
摘要：
本文证明了Griffiths双锥空间的基本群与三锥空间的基本群同构。更一般地，若$\kappa$是满足$2 \leq \kappa\leq 2^{\aleph_0}$的基数，则$\kappa$重锥空间与双锥空间具有相同的基本群。所得同构是非构造性的，且当$2 < \kappa$时，2重锥与$\kappa$重锥的基本群之间不存在可通过连续映射实现的同构。我们还证明了James W. Cannon与Gregory R. Conner的一个猜想，即Griffiths双锥空间的基本群与调和群岛（harmonic archipelago）的基本群同构。
英文摘要：
It is shown that the fundamental group of the Griffiths double cone space is isomorphic to that of the triple cone. More generally if $κ$ is a cardinal such that $2 \leq κ\leq 2^{\aleph_0}$ then the $κ$-fold cone has the same fundamental group as the double cone. The isomorphisms produced are non-constructive, and no isomorphism between the fundamental group of the $2$- and of the $κ$-fold cones, with $2 < κ$, can be realized via continuous mappings. We also prove a conjecture of James W. Cannon and Gregory R. Conner which states that the fundamental group of the Griffiths double cone space is isomorphic to that of the harmonic archipelago.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
