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Diagonal transformations in quadrangulations of surfaces

โœ Scribed by Nakamoto, Atsuhiro

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
546 KB
Volume
21
Category
Article
ISSN
0364-9024

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โœฆ Synopsis

In this paper, it will be shown that any two bipartite quadrangulations of any closed surface are transformed into each other by two kinds of transformations, called the diagonal slide and the diagonal rotation, up to homeomorphism, if they have the same and sufficiently large number of vertices.

๐Ÿ“œ SIMILAR VOLUMES

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In this paper, we shall show that any two quadrangulations on any closed surface can be transformed into each other by diagonal slides and diagonal rotations if they have the same and sufficiently large number of vertices and if the homological properties of both quadrangulations coincide.

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Consider a class P of triangulations on a closed surface F 2 , closed under vertex splitting. We shall show that any two triangulations with the same and sufficiently large number of vertices which belong to P can be transformed into each other, up to homeomorphism, by a finite sequence of diagonal