# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [1] W.P. Baritompa, The space of edge-weighted trees is a Euclidean cell for trees with exactly one interior vertex, Report No. UCDMS2003/3, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand, 2003 [2] Billera, L.J.; Holmes, S.P.; Vogtmann, K., Geometry of the space of phylogenetic trees, Adv. in appl. math., 27, 4, 733-767, (2001) · Zbl 0995.92035 [3] Björner, A., Topological methods, (), 1819-1872 · Zbl 0851.52016 [4] Björner, A.; Las Vergnas, M.; Sturmfels, B.; White, N.; Ziegler, G., Oriented matroids, (1993), Cambridge Univ. Press Cambridge · Zbl 0773.52001 [5] Felsenstein, J., Inferring phylogenies, (2004), Sinauer Press Sunderland, MA [6] Gill, J., The k-assignment polytope and the space of evolutionary trees, licentiate thesis, linköping studies in science and technology, (2004), Thesis No. 1117, available at [7] Haver, W., A characterization theorem for cellular maps, Bull. amer. math. soc., 76, 1277-1280, (1970) · Zbl 0205.27901 [8] Kim, J., Slicing hyperdimensional oranges: the geometry of phylogenetic estimation, Molecular phyl. evol., 17, 58-75, (2000) [9] Moulton, V.; Steel, M., Peeling phylogenetic ‘oranges’, Adv. in appl. math., 33, 710-727, (2004) · Zbl 1067.92045 [10] Munkres, J., Topology, (1999), Pearson Education [11] Quinn, F., Ends of maps III: dimensions 4 and 5, J. differential geom., 17, 503-521, (1982) · Zbl 0533.57009 [12] Semple, C.; Steel, M., Phylogenetics, (2003), Oxford Univ. Press Oxford · Zbl 1043.92026 [13] C. Tuffley, Trees and Ps and things that sneeze: Markov process models of site substitution, MSc thesis, University of Canterbury, Christchurch, New Zealand, 1997
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.