Framed Cobordism

Some articles on framed cobordism, framed, cobordism:

The Arf Invariant in Topology - Examples
... This can also be viewed as the framed cobordism class of with this framing in the 1-dimensional framed cobordism group, which is generated by the circle with the Lie group framing ... The Arf invariant of the framed surface is now defined Note that, so we had to stabilise, taking to be at least 4, in order to get an element of ... The Arf invariant of a framed surface detects whether there is a 3-manifold whose boundary is the given surface which extends the given framing ...
Homotopy Groups Of Spheres - General Theory - Framed Cobordism
... Homotopy groups of spheres are closely related to cobordism classes of manifolds ... established an isomorphism between the homotopy group πn+k(Sn) and the group Ωkframed(Sn+k) of cobordism classes of differentiable k-submanifolds of ... → Sn is homotopic to a differentiable map with a framed k-dimensional submanifold ...

Famous quotes containing the word framed:

    In 1845 he built himself a small framed house on the shores of Walden Pond, and lived there two years alone, a life of labor and study. This action was quite native and fit for him. No one who knew him would tax him with affectation. He was more unlike his neighbors in his thought than in his action. As soon as he had exhausted himself that advantages of his solitude, he abandoned it.
    Ralph Waldo Emerson (1803–1882)