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Title: Maps on surfaces with boundary
Author: Bryant, Robin Phillip
ISNI:       0000 0001 3506 6323
Awarding Body: University of Southampton
Current Institution: University of Southampton
Date of Award: 1984
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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 modular group and with an illustrative example.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Pure mathematics