The isotopy group of the integral octonions is the perfect double cover of the group of rotations of the E 8 lattice.
32.
Legendrian submanifolds are very rigid objects; typically there are infinitely many Legendrian isotopy classes of embeddings which are all smoothly isotopic.
33.
There are quasi-conformal mappings in every isotopy class and so an alternative definition for The Teichm�ller space is as follows.
34.
In fact, there should be an isotopy of the plane that maps any such curve onto [ 0, 1 ].
35.
However, up to isotopy, the space of symplectic structures is discrete ( any family of symplectic structures are isotopic ).
36.
I'll put a reference to this under isotopy . talk ) 11 : 58, 17 November 2010 ( UTC)
37.
No other part of the diagram is involved in the picture of a move, and a planar isotopy may distort the picture.
38.
In geometric topology & mdash; for example in knot theory & mdash; the idea of isotopy is used to construct equivalence relations.
39.
Using pseudo-holomorphic curves, and associated a bigraded abelian group, called knot Floer homology, to each isotopy class of knots.
40.
A cobordism argument can be used to show that this homology class is independent of the choice of \ omega, up to isotopy.
