Balagopalan, Sonia
(2014)
Some Results on
Vertex-Minimal Triangulations of
Manifolds.
PhD thesis, National University of Ireland Maynooth.
Abstract
This thesis presents some results on vertex-minimal (simplicial) triangulations
of manifolds. We are interested in triangulations that have nice geometric and
combinatorial properties.
In the first chapter, we list some defnitions used throughout the thesis.
In the second chapter, we give an elementary construction of the Witt design
on 22 points, and a combinatorial description of the only known vertex-minimal
triangulation of real projective 4-dimensional space. We show that the 16-vertex
complex we describe triangulates RP4 by constructing a 4-dimensional combinatorial
sphere which can be easily seen to be a double cover of our complex.
In the third chapter, we give two geometric constructions of the 16-vertex
RP4.
In the fourth chapter, we give a purely combinatorial description of a 15-vertex
triangulation of an 8-manifold that has the same cohomology as the quaternionic
projective plane HP2, and is conjectured to be homeomorphic to HP2.
| Item Type: |
Thesis
(PhD)
|
| Keywords: |
Vertex-Minimal Triangulations; Manifolds; |
| Academic Unit: |
Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: |
5024 |
| Depositing User: |
IR eTheses
|
| Date Deposited: |
12 Jun 2014 14:45 |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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