Topological approaches to tree reconstruction

CREATED: 200908170719 sequences $\rightarrow$ distances $\rightarrow$ tree sequences $\rightarrow$ splits $\rightarrow$ tree

Idea: instead of going from distances/splits to trees, from distances/splits to topological spaces first

$S$: set of species $D$: distances between two species The tight span $T_D$ is ${ f : S \rightarrow R | f(x) + f(y) \geq D(x,y) }_\min$.

$C$ are the cut faces of the complex polytope.

Buneman complex for a system of splits.