## Tags » Low-dimensional Topology

#### Hyperbolic Knots

*Ref:Cromwell

A knot is called a hyperbolic knot if its complement is a hyperbolic space. Recall that a surface is called hyperbolic if it admits a Riemannian metric such that the Gaussian curvature is identical to . 375 more words

Low-Dimensional Topology

*Ref: Cromwell

### Satellite Construction

We first define some terms for links.

Definition 1:

A link is called a spilt linkĀ if there exists embedded in such that the sphere separate into two connected component and such that one component of is in , the other one is in .

1,239 more words
Low-Dimensional Topology

*Ref : Cromwell

We should like to deal with links in a 2-dimensional sense. A linking diagram is a graph that contains the information of crossings of a link, and we can recover the original link by just looking at the 2-dimensional diagram. 1,457 more words

Low-Dimensional Topology

#### A little bit of Surgery and Loops

*Reference: Cromwell

Definition 1:

A connected component of the boundary of a manifold is called a boundary component.

The boundary components are the black loops…

630 more words
Low-Dimensional Topology

#### Torus Knots

This are the knots that live on the torus surface.

A torus surface looks like

We can generate a torus by taking a circle on the -plane of radius r with center on -axis at distance from the origin, then rotate it around -axis. 342 more words

Low-Dimensional Topology

#### Basic Concepts of Knots and Links

*Reference: Cromwell – Knots and Links