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Results tagged with kt.k-theory-and-homology
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user 16785
Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
10
votes
Accepted
$K$-homology of $BG$
In "$K$-homology of universal spaces and local cohomology of the representation ring" Greenlees proves that
$$
K_i(BG_+) \simeq H_J^i(R(G))
$$
for $i=0,1$, where $J$ is the augmentation ideal and $H_ …
- 3,784
9
votes
Accepted
$K_3(\mathbb{Z})$ and $\pi ^S_3$
We have $\pi_3(\mathbb{S}) \cong \mathbb{Z}/24\{ \nu\}$ and $\pi_3K(\mathbb{Z}) \cong \mathbb{Z}/48\{ \lambda \}$. As Achim suggested, the unit map $\mathbb{S} \to K(\mathbb{Z})$ induces on $\pi_3$ th …
- 3,784
3
votes
Accepted
A set of objects classically generates the full subcategory of compact objects iff it genera...
I agree that the various notions of 'generates' can be confusing. I think the following result may clarify what you are after (this can be found in Lemma 2.2.1 of 'Stable model categories are categori …
- 3,784