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Results tagged with homotopy-theory
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Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
5
votes
Is this true of the frame bundle $\operatorname{Fr}(M)$?
There is a tiny confusion of language here. If you are talking about the orthonormal frame bundle you have a Riemannian manifold not just a manifold. The frame bundle has structure group $Gl_n(\math …
- 3,439
11
votes
Teaching Steenrod Operations
Its nice to look also at Bott's early paper
"On symmetric products and the Steenrod squares. "
Ann. of Math. (2) 57, (1953). 579–590.
He uses an early version of Smith theory. Depending on how
you …
- 3,439
45
votes
third stable homotopy group of spheres via geometry?
This is really a comment try to make clear the point Tilman was trying to make
but it is too long.
A K3 surface has trivial canonical bundle (after all that and simple connectivity is the definition) …
- 3,439
9
votes
Proofs of Bott periodicity
There is also Atiyah and Singer's proof in
"Index theory for skew-adjoint fredholm operators"
Inst. Hautes Études Sci. Publ. Math. No. 37 1969 5–26.
57.50
This proof uses Kuiper's theorem on the co …
- 3,439