Resumen de The moduli space of n tropically collinear points in Rd
The tropical semiring (R,min,+) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled npoint configurations lying on a tropical line in dspace, which is interpretable as the space of nspecies phylogenetic trees. This is equivalent to the space of n × d matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension d = 3 and compute its homology in this case, conjecturing that this complex is shellable in general. We also investigate the space of d × n matrices of Barvinok rank two, a subcomplex directly related to optimization, giving a complete description of this subcomplex in the case d = 3.
