@Article{CMR-32-375,
author = {Sun , Dongqi},
title = {Subsurface 1-Distance of the Handlebody},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {32},
number = {4},
pages = {375--382},
abstract = {<p style="text-align: justify;">For a handlebody $H$ with $∂H = S$, let $F ⊂ S$ be an essential connected
subsurface of $S$. Let&nbsp;$\mathcal{C}(S)$ be the curve complex of $S$,&nbsp;$\mathcal{AC}(F)$ be the arc and curve
complex of $F$,&nbsp;$\mathcal{D}(H) ⊂&nbsp;\mathcal{C}(S)$ be the disk complex of $H$ and $π_F (\mathcal{D}(H)) ⊂&nbsp;\mathcal{AC}(F)$ be
the image of&nbsp;$\mathcal{D}(H)$ in&nbsp;$\mathcal{AC}(F)$. We introduce the definition of subsurface 1-distance
between the 1-simplices of $\mathcal{AC}(F)$ and show that under some hypothesis, $π_F (\mathcal{D}(H))$
comes within subsurface 1-distance at most 4 of every 1-simplex of $\mathcal{AC}(F)$.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.13447/j.1674-5647.2016.04.09},
url = {http://global-sci.org/intro/article_detail/cmr/18909.html}
}