Year: 2018
Type: preprint
Abstract: Let $X$ be a contractible $2$-complex which is a union of two contractible subcomplexes $Y$ and $Z.$ Is the intersection $Y\cap Z$ contractible as well? In this note, we prove that the inclusion-induced map $π_{1}(Y\cap Z)\rightarrow π_{1}(Z)$ is injective if $Y$ is $π_{1}$-injective subcomplex in a locally CAT(0) 2-complex $X$. In particular, each component in the intersection of two contractible subcomplexes in a CAT(0) 2-complex is contractible.
Source: arXiv (Cornell University)
Authors: Ji, Feng, Ye, Shengkui
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2896010787