Algebraic Topology
The five or six (depending on the status of n=126) (framed cobordism classes of) manifolds of Kervaire invariant one, which exist in dimension for and possibly 126, but no higher, are exceptional objects related to exotic spheres. It is conjectured that these are related to the Rosenfeld projective planes (over octonions and related) and exceptional Lie algebras, due to similarities of dimensions, but no connection has been established.
Read more about this topic: Exceptional Object
Famous quotes containing the word algebraic:
“I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”
—Henry David Thoreau (1817–1862)