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I discovered that we have this old entry. Have now polished it up a little, cross-linked it with pointed category and pointed model category and with the entries that have been referring to this term all along, without linking to it, which includes stable (∞,1)-category and Toda bracket.
I have added the quote:
As is well known, it is our manifest destiny as 21st century algebraic topologists to compute homotopy groups of spheres. (Wilson 13, p. 1)
brief category:people-entry for hyperlinking references at D=11 supergravity
brief category:people-entry for hyperlinking references at D=11 supergravity
brief category:people-entry for hyperlinking references at cohomotopy
brief category:people-entry for hyperlinking references at Adams-Novikov spectral sequence
I have adjusted the second paragraph of the Idea-section to make it read more smoothly (hopefully); and I provided it with explicit pointer to where in Novikov’s article the MU-sequence and its convergence is actually stated:Novikov 67, Theorems 3.1, 3.3.
Also added pointer to
and to
one more in the list of entries on n-spheres, now to satisfy links needed at the octonionic version of the AKM-theorem
brief category:people-entry for hyperlinking references at AKM-theorem
for completeness (to go alongside complex projective plane and octonionic projective plane) and in order to give a home to the statement of the quaternionic AKM-theorem
brief category:people-entry for hyperlinking references at surgery theory
stub for constructible sheaf
on Pontryagin’s identification of unstable Cohomotopy of closed manifolds with cobordism classes of their normally framed submanifolds – to go alongside Thom’s theorem (which is originally the analogous statement but for oriented submanifolds and maps into a universal -Thom space) and the Pontryagin-Thom construction (which has come to be the term used for all kinds of generalizations and variants that neither Pontryagin nor Thom probably ever dreamed of).
For the moment the bulk of the material is copied over from the existing section at Cohomotopy, but I hope to improve a bit on this a little later.
brief category:people-entry for hyperlinking references at Pontryagin’s theorem
I have finally dug out
which has English translations of Pontryagin’s old articles, like the one with the famous mistake and the one with the famous fix of the mistake.
So I have added the pointer here, and expanded the commentary around it a little.
brief category:people-entry for hyperlinking references at homotopy groups of spheres
I have added a subsection Applications – In Cohomotopy and Cobordism theory highlighting how the properness of maps from compact to Hausdorff spaces is what makes the unstable Pontryagin-Thom isomorphism tick – for closed (hence compact) manifolds.
(This seems profound enough an example to justify mentioning. Also, it’s a point that tends to get lost in accounts of the theorem…)
This is a page with fully explicit component computations of properties of the Hodge star operator on Minkowski spacetime. It is a bare sub-section, to be !include-ed inside sections of relevant entries (under “Examples” at Hodge star operator and under “Properties” at Minkowski spacetime)
created stub for Pfaffian line bundle, because I needed the link to the entry and to the single reference currently given there. Will fill in more details later today.
In the course of this I also created an extremely stubby entry fermion.
brief category:people-entry for hyperlinking references at AdS-CFT correspondence
added pointer to:
stub for Landweber exact functor theorem, to be expanded
added pointer to
and re-arranged the references slightly, moving those on supersymmetry to a dedicated subsection
a bare list of references, to be !include-ed inside the lists of references of relevant entries, such as at D=6 N=(2,0) SCFT, functorial field theory and extended TQFT
created Thom’s transversality theorem
A stub, to provide a home for today’s
For discussion at geometry of physics I need a way to point to the concept of “locality” in QFT, so I gave it a small entry: local quantum field theory.
brief category:people-entry for hyperlinking references at Khovanov homology, movie and elsewhere
A stub.
I was looking for a canonical reference to go with the term “movie” in relation to higher dimensional bordisms/tangles/knots. Preferably with the words like “A movie of … is …”.
For the moment I just have a pointer to the original Carter-Saito 93
am splitting this off as a stand-alone statement (from complex projective space)
Have cleaned-up the formulation of statement and proof and have generalized from ground ring the complex numbers to reals, complex numbers and quaternions.