论文标题
Griffiths双锥组是三倍的同构
The Griffiths double cone group is isomorphic to the triple
论文作者
论文摘要
结果表明，格里菲斯双锥形空间的基本组与三锥体的基础是同构。通常，如果$κ$是红衣主教，使得$ 2 \ leqκ\ leq 2^{\ aleph_0} $，那么$κ$ -fold锥体具有与双锥相同的基本组。产生的同构是非构造性的，$ 2 $的基本组和$κ$ - 折叠的圆锥（$ 2 <κ$）之间没有同构性，可以通过连续映射实现。我们还证明了詹姆斯·W·坎农（James W. Cannon）和格雷戈里·R·康纳（Gregory R.
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.
