Timeline for Understanding the product in topological K-theory
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2010 at 18:23 | comment | added | Tyler Lawson | On that page he actually says $K(S^2)$ has that form, not the reduced K-theory $\tilde K(S^2)$. In this case $\alpha$ is $H-1$, and in particular it's a virtual bundle rather than coming from an actual bundle. $H$ is the one that comes from an actual bundle. | |
| Jan 29, 2010 at 14:44 | comment | added | roger123 | Hatcher says in 2.3. page 60 that $\tilde{K}(S^2)$ is $\mathbb{Z}[\alpha]/\alpha^2$. Because he pulls alpha back it has to be a vector bundle and not only a virtual one but what is $\alpha$ then? Isn't $H-1$ just a virtual bundle? | |
| Jan 29, 2010 at 11:09 | vote | accept | roger123 | ||
| Jan 28, 2010 at 22:10 | comment | added | roger123 | ah, so $S^0$ is really an exception! $\tilde{K}(S^{2n})\cong \mathbb{Z}$ for all $n\geq 0$ as a group and as a ring for $n=0$ but for $n>1$ the ring structure is trivial. This helps me much. Thank you. | |
| Jan 28, 2010 at 20:55 | comment | added | Tyler Lawson | err, yes. I'm not sure why I wrote it like that. edited. | |
| Jan 28, 2010 at 20:54 | history | edited | Tyler Lawson | CC BY-SA 2.5 |
more dopiness.
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| Jan 28, 2010 at 20:52 | comment | added | Mariano Suárez-Álvarez | The ideal of $\mathbb Z[H]/(H-1)^2$ generated by $H-1$, no? | |
| Jan 28, 2010 at 20:47 | history | answered | Tyler Lawson | CC BY-SA 2.5 |