从射影平面的同胚群到特殊正交群的强等变形变收缩
A strong equivariant deformation retraction from the homeomorphism group of the projective plane to the special orthogonal group
摘要：
这是关于定向拟阵和Grassmannians系列的第三篇论文。我们构造了一个从2-球面的同胚群到$\mathrm{O}_3$的$(\mathrm{O}_3\times\mathbb{Z}_2)$ -等变强形变收缩，其中$\mathbb{Z}_2$的作用由作用在右边的对映反射产生，而$\mathrm{O}_3$作用在左边的等距反射.对映映射的商化导致从射影平面的同胚群到$\mathrm{SO}_3$的$\mathrm{SO}_3$ -等变强形变收缩.这同样适用于保持空集系统的同胚子群。这证实了玛丽-伊丽莎白·哈姆斯特伦的一个猜想。
英文摘要：
This is the third paper in a series on oriented matroids and Grassmannians. We construct a $(\mathrm{O}_3\times\mathbb{Z}_2)$-equivariant strong deformation retraction from the homeomorphism group of the 2-sphere to $\mathrm{O}_3$, where the action of $\mathbb{Z}_2$ is generated by antipodal reflection acting on the right, and $\mathrm{O}_3$ acts on the left by isometry. Quotienting by the antipodal map induces a $\mathrm{SO}_3$-equivariant strong deformation retraction from the homeomorphism group of the projective plane to $\mathrm{SO}_3$. The same holds for subgroups of homeomorphisms that preserve the system of null sets. This confirms a conjecture of Mary-Elizabeth Hamstrom.
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。
