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Results tagged with stable-homotopy
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user 184
Stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.
13
votes
0
answers
665
views
A tensor product for triangulated categories?
Many triangulated categories which show up in mathematics, such as derived categories of various sorts, arise as the homotopy category of a stable $\infty$-category.
Stable $\infty$-categories give …
- 27.5k
8
votes
Accepted
Are there universe-indexed spectra over simplicial sets?
Yes to both interpretations of your question. It is not clear to me where you want to put pointed simplicial sets.
One interpretation of your question is that you want to replace pointed topological …
- 27.5k
14
votes
0
answers
788
views
How to see the quaternionic hopf map generates the stable 3-stem?
I am looking for a direct proof that the quaternionic hopf map generates (after suspension) the 3rd stable homotopy group of spheres. There are some related MO questions, for example:
third-stable-h …
- 27.5k
7
votes
Accepted
Categorical models for truncations of the sphere spectrum
I don't understand what you mean about the "directed sphere" so will focus on the other questions.
The free Picard $n$-category on one object has a description as a bordism $n$-category. Specifically …
- 27.5k
28
votes
Accepted
Nilpotence of the stable Hopf map via framed cobordism
Answer Summary
Let $\eta$ be the framed 1-manifold which is the Lie group framing on the circle and let $\nu$ be the Lie group framing on $S^3 = Spin(3)$. I am probably going to conflate these framed …
- 27.5k
66
votes
1
answer
2k
views
Is there an octonionic analog of the K3 surface, with implications for stable homotopy group...
The infamous K3 surface has many constructions in many fields ranging from algebraic geometry to algebraic topology. Its many properties are well known. For this question I am really interested in the …
- 27.5k