Alexander Polynomial - Relations To Satellite Operations

Relations To Satellite Operations

If a knot is a satellite knot with companion i.e.: there exists an embedding such that where is an unknotted solid torus, then . Where is the integer that represents in .

Examples: For a connect-sum . If is an untwisted Whitehead double, then .

Read more about this topic:  Alexander Polynomial

Famous quotes containing the words relations, satellite and/or operations:

    Subject the material world to the higher ends by understanding it in all its relations to daily life and action.
    Ellen Henrietta Swallow Richards (1842–1911)

    Books are the best things, well used; abused, among the worst. What is the right use? What is the one end, which all means go to effect? They are for nothing but to inspire. I had better never see a book, than to be warped by its attraction clean out of my own orbit, and made a satellite instead of a system.
    Ralph Waldo Emerson (1803–1882)

    It may seem strange that any road through such a wilderness should be passable, even in winter, when the snow is three or four feet deep, but at that season, wherever lumbering operations are actively carried on, teams are continually passing on the single track, and it becomes as smooth almost as a railway.
    Henry David Thoreau (1817–1862)