15
votes
Accepted
Are Spanier-Whitehead duals of general spaces expressible through some generalization of normal bundles?
Let $X$ be a finite complex. Then the functor
$$\lim_X:\operatorname{Fun}(X,\operatorname{Sp})\to \operatorname{Sp}$$
sending a local system of spectra $E$ to its limit preserves all colimits. Indeed ...
- 16.5k
6
votes
Accepted
Is $\Sigma^\infty_+ O(n)^\vee$, the Spanier-Whitehead dual of the orthogonal group, an $A_\infty$-ring spectrum?
The question as stated probably requires clarification. If
$X$ is a space, then the S-dual $D_+(X)$ (i.e., functions from $X_+$ to the sphere) is always an $E_\infty$-ring spectrum. In particular, it ...
- 18.8k
Only top scored, non community-wiki answers of a minimum length are eligible