| dc.creator |
Dona, Luca
|
| dc.date.accessioned |
2007-05-09T20:14:37Z |
| dc.date.available |
2007-05-09T20:14:37Z |
| dc.date.issued |
1995 |
| dc.identifier.uri |
http://hdl.handle.net/1911/16814
|
| dc.description.abstract |
Tools and techniques in hyperbolic geometry are developed and applied primarily to questions about intersections of curves on surfaces. Formulae which explicitly relate the coefficients of a matrix to the geometric data of a hyperbolic transformation are found and applied. A purely algebraic general criterion for an element to be simple is found. Particularly convenient representations of Fuchsian groups are discussed. These representations have coefficients which belong to a ring with integral coefficients, and have nice symmetry properties. As a result, an algorithm to recover the word of a matrix in terms of the generating elements is given. Also, the general criterion for simplicity previously found is further reduced to a system of diophantine equations. In the appendices, another purely combinatorial algorithm for loops on surfaces is given, as well as a short proof of Dehn's solution to the word problem, and a proof that a system of simple non-parallel curves on a surface, where each pair are allowed to intersect at most k times, is finite. |
| dc.format |
PDF |
| dc.format.mimetype |
application/pdf |
| dc.language.iso |
eng |
dc.subject |
Mathematics
|
| dc.title |
Hyperbolic geometry, regular representations and curves on surfaces |
| dc.type.genre |
Thesis |
| dc.type.material |
Text |
| thesis.degree.discipline |
Mathematics |
| thesis.degree.grantor |
Rice University |
| thesis.degree.level |
Doctoral |
| dc.identifier.citation |
Dona, Luca. "Hyperbolic geometry, regular representations and curves on surfaces." Doctoral Thesis, Rice University, ETD http://hdl.handle.net/1911/16814. |
