share
12 มีนาคม 2021, 10:08
a tangle is generally one of two related concepts:
In John Conway's definition, an n-tangle is a proper embedding of
the disjoint union of n arcs into a 3-ball;
the embedding must send the endpoints of the arcs to 2n
marked points on the ball's boundary.
In link theory, a tangle is an embedding of n arcs and m circles
into R^2 X [0,1] the difference from the previous definition
is that it includes circles as well as arcs,
and partitions the boundary into two (isomorphic) pieces,
which is algebraically more convenient
it allows one to add tangles by stacking them, for instance.
In John Conway's definition, an n-tangle is a proper embedding of
the disjoint union of n arcs into a 3-ball;
the embedding must send the endpoints of the arcs to 2n
marked points on the ball's boundary.
In link theory, a tangle is an embedding of n arcs and m circles
into R^2 X [0,1] the difference from the previous definition
is that it includes circles as well as arcs,
and partitions the boundary into two (isomorphic) pieces,
which is algebraically more convenient
it allows one to add tangles by stacking them, for instance.