Affine Maps That Induce Polyhedral Complex Isomorphisms |
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| Authors: | A Dress K T Huber V Moulton |
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| Institution: | (1) FSPM-Strukturbildungsprozesse, University of Bielefeld, D-33501 Bielefeld, Germany dress@mathematik.uni-bielefeld.de , DE;(2) Institute of Fundamental Sciences, Massey University, Private Bag 11 222, Palmerston North, New Zealand kathi@dirac.fmi.mh.se , NZ;(3) FMI, Mid Sweden University, Sundsvall S-851 70, Sweden vince@dirac.fmi.mh.se, SE |
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| Abstract: | In this paper we show that an affine bijection f : T
1
→ T
2
between two polyhedral complexes T
1
,T
2
, both of which consist of a union of faces of two convex polyhedra P
1
and P
2
, necessarily respects the cell-complex structure of T
1
and T
2
inherited from P
1
and P
2
, respectively, provided f extends to an affine map from P
1
into P
2
. In addition, we present an application of this result within the area of T-theory to obtain a far-reaching generalization
of previous results regarding the equivalence of two distinct constructions of the phylogenetic tree associated to ``perfect'
(that is, treelike) distance data.
Received September 30, 1999, and in revised form February 25, 2000. Online publication May 15, 2000. |
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| Keywords: | |
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