Questions tagged [stable-homotopy-theory]
203 questions
3
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stable homotopy groups zero
A connected CW-complex $X$ is contractible iff the homotopy groups $\pi_n(X)$ are zero for all $n\geq 1$.
What (if any?) is the analogous statement for the vanishing of all stable homotopy groups $\pi_n^S(X)$ for all $n\geq 1$ ?
More generally,…
user68316
- 461
2
votes
2 answers
Solving Recursions Without Initial Conditions
I am trying to solve the following recursion but it does not appear that I can use characteristic equations or generating functions since I do not have initial conditions. Is there another way I am missing or can I assume initial conditions to use…
user71443
- 223
1
vote
1 answer
Degree of a pmap
Today I have started reading stable homotopy. I have came across the notion of a pmap which is basically equivalence class of maps from cofinal sub-spectra. My query is what do we mean by degree of such map?
Tritte
- 31
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Filtration of the category of finite spectra
Consider the stable homotopy category $\mathcal{SHC}$, we then can define its full subcategory $\mathcal{SHC}^c$ spanned by finite spectra which coincides with the smallest thick triangulated subcategory of $\mathcal{SHC}$ generated by…
N.B.
- 2,109
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The Relationship Between Two Constructions of Topological Modular Forms
There are two explicit constructions of topological modular forms. One is in the 12th section of the book $Topological$ $Modular$ $Forms$, and the other is Lurie's Elliptic Cohomology II in his homepage. More precisely speaking, they both defined…
user884626
- 149
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