Bryant, Robin Phillip (1984) Maps on surfaces with boundary. University of Southampton, Doctoral Thesis.
Abstract
The thesis begins by reviewing the classical theory of maps on orientable surfaces without boundary. The concept of a map is extended to include imbeddings in both non-orientable surfaces and surfaces with boundary. The idea of a blade is introduced and permutations of these objects defined. The group generated by these permutations is a homomorphic image of an extended triangle group. Subgroups of these groups are non-Euclidean crystallographic groups and a proof is given of a result concerning their signatures. The thesis shows that given any such permutations, with suitable restrictions, an appropriate map can be reconstructed on a surface with boundary. A natural extension of the classical Euler-Poincare characteristic is given which applies to maps on surfaces with boundary. The thesis concludes with a simple application to the excer.de.i modular group and with an illustrative example.
This record has no associated files available for download.
More information
Identifiers
Catalogue record
Export record
Contributors
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.