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Results tagged with stable-homotopy
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user 163893
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.
26
votes
1
answer
828
views
Are complex-oriented ring spectra determined by their formal group law?
To every complex-oriented ring spectrum $E$ there is associated a formal group law, which is a power series $F_E(x,y)\in E_*[[x,y]]$.
Suppose $E$ and $F$ are two complex-oriented ring spectra and supp …
- 2,052
16
votes
3
answers
775
views
"Phantom" non-equivalences of spectra?
I would like an example of the following situation, or a proof that no such example exists.
$\textbf{Situation}$: Two connective (EDIT: I'm fine with dropping this condition) spectra $X$ and $Y$ such …
- 2,052
9
votes
Accepted
Does a Gysin map depend on the choice of Thom class?
Yes it does! The map in your display is (more or less) the cup product with the Thom class $\lambda_N$. So if you choose a different Thom class you'll get a different map.
For example, take the standa …
- 2,052
4
votes
"Phantom" non-equivalences of spectra?
Here's a connective example. It is also an example of Maxime's variant question in the comments (regarding $\tau_{\leq m}$ truncations). And thanks to Maxime for looking this argument over before I po …
- 2,052