Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Thanks. BTW, it’s spelled [[norm topology]]
, with square brackets around it.
Sorry :-)
Interesting to look at the time stamps:
In Feb 2012 Uribe et al. pick up the topic and amplify (Sec. 1) the wrong statement from Atiyah-Segal.
In Sept 2013 Schottenloher points out the issue.
In Nov 2013 Uribe et al.’s article gets published.
In July 2014 Uribe at al.-prime notice the issue, apparently still unaware of Schottenloher’s preprint (?).
In Aug 2014 Uribe et al.-prime is already published, too.
In 2015 nothing happens.
In 2016 nothing happens.
In 2017 nothing happens.
In Aug 2018 (a rewrite of) Schottenloher’s preprint is finally published.
What gives?
One wonders why Atiyah-Segal made the error. An early sign of what was to come?
I tried to really in-depth read the twisted K-theory paper as a PhD student, and it was so brief on details in certain places I made no headway for a long time, and eventually gave up. A number of reasons for this, but certainly having mistakes like the one under discussion doesn’t help!
One wonders why Atiyah-Segal made the error.
People make mistakes all the time. Authorities do, too.
added the statement that $U(\mathcal{H})$ in the strong topology is completely metrizable, with pointer to:
added pointer to
for a proof that the weak and strong topology on $U(\mathcal{H})$ agree and make it a topological group
added the statement that $U(\mathcal{H})_{strong}$ is not locally compact, with reference to section 5 in:
Is $\mathrm{U}(\mathcal{H})$ well-pointed?
I know that
$S^1$ is well-pointed;
$\mathrm{PU}(\mathcal{H})$ is well-pointed;
there is an open neighbourhood $V_{\mathrm{e}}$ of $\mathrm{e}$ in $PU(\mathcal{H})$ such that
$\mathrm{U}(\mathcal{H})_{\vert V_{\mathrm{e}}} \simeq V_{\mathrm{e}} \times S^1$
products of h-cofibrations remain h-cofibrations.
This seems like it might be getting close. Or maybe not.
[ edit: on the other hand, it dawns on me that I don’t actually need to know the answer to do what I want to do… ]
I have spelled out the various topologies, following the list as given by Espinoza & Uribe. Then I have further refined the list of propositions about these topologies, with references.
It seems that all these results, except maybe concerning the compact-open topology, are already due to K-H Neeb in the 1990s.
1 to 13 of 13