Representing 3-manifolds by triangulations of S³: a constructive approach
A triangulation Δ of S³ defines uniquely a number m ≤ 4; a subgraph T of Δ and a representation ω(Δ) of Π1(S³\T) into Σm: It is shown that every (K,ω), where K is a knot or link in S³ and ω is transitive representation of Π1(S³\K) in Σm, 2 ≤ m ≤ 3, equals ω(Δ), for some Δ. From this, a representation of closed, orientable 3-manifolds by triangulations of S³ is obtained. This is a theorem of Izmestiev and Joswig, but, in contrast with their proof, the methods in this paper are constructive. Some generalizations are given. The method involves a new representation of knots and links, which is called a butter y representation.
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2005
|
| Online Access: | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262005000200001 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|