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A regular decomposition of the edge-product space of phylogenetic trees. (English) Zbl 1149.05305
Summary: We investigate the topology and combinatorics of a topological space called the edge-product space that is generated by the set of edge-weighted finite labelled trees. This space arises by multiplying the weights of edges on paths in trees, and is closely connected to tree-indexed Markov processes in molecular evolutionary biology. In particular, by considering combinatorial properties of the Tuffley poset of labelled forests, we show that the edge-product space has a regular cell decomposition with face poset equal to the Tuffley poset.

MSC:
05C05 Trees
92D15 Problems related to evolution
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