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- W2891478487 abstract "In this work, we study the cellular decomposition of $S$ induced by a filling pair of curves $v$ and $w$, $Dec_{v,w}(S) = S - (v cup w)$, and its connection to the distance function $d(v,w)$ in the curve graph of a closed orientable surface $S$ of genus $g$. Efficient geodesics were introduced by the first author in joint work with Margalit and Menasco in 2016, giving an algorithm that begins with a pair of non-separating filling curves that determine vertices $(v,w)$ in the curve graph of a closed orientable surface $S$ and computing from them a finite set of efficient geodesics. We extend the tools of efficient geodesics to study the relationship between distance $d(v,w)$, intersection number $i(v,w)$, and $Dec_{v,w}(S)$. The main result is the development and analysis of particular configurations of rectangles in $Dec_{v,w}(S)$ called spirals. We are able to show that, in some special cases, the efficient geodesic algorithm can be used to build an algorithm that reduces $i(v,w)$ while preserving $d(v,w)$. At the end of the paper, we note a connection of our work to the notion of extending geodesics." @default.
- W2891478487 created "2018-09-27" @default.
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- W2891478487 date "2018-09-19" @default.
- W2891478487 modified "2023-09-27" @default.
- W2891478487 title "Distance and intersection number in the curve graph of a surface" @default.
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