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.
I have started an entry on proper homotopy theory. This is partially since it will be needed in discussing some parts of strong shape theory, but it may also be useful for discussing duality and various other topics, including studying non-compact spaces in physical contexts. This is especially true for non-compact manifolds. (I do not know what fibre bundles etc. look like in the proper homotopy setting!)
I have added more material here. So far I have defined the proper homotopy category, and have started discussing ends. (not categorical ones, topological ones).
I have put a query box about the space of ends as a maximal ideal space of some ring. Thought I should draw attention to it, as I am at a loss to see the analogue between the proper theory here and analogues in algebraic geometry. Anyone any ideas?
Question at proper homotopy theory about a typo I can’t fix.
@David. I can’t figure out what your question is? Doh!
A subspace A in X is cofinal if its complement is sort of compact, but as we want allow for A to be closed in X we take the closure of the complement cl(X-A). Am I reading what I want rather than what I wrote, somehow?
That’s it, I think. There was a $W$ which should have been an $X$, I think. I sort of figured it out afterwards, but I wanted to be sure.
I’ve edited the page and removed my comment.
I wanted X so I read X. Here I have just got up and I forgot to switch my eyes on!!!!!!! Double doh!
I have created an entry on the Brown-Grossman homotopy groups. This contains (will contain once I have typed it!) a statement of the Whitehead theorem in this setting. This gives neat conditions globally and at the ends for a map to be a proper homotopy equivalence.
Igor Khavkine has recreated the entry Proper Homotopy Theory. The old copy gave an error message, (Application error (Apache)
Something very bad just happened. I just know it. Do you smell smoke?) I would rename his copy to be the main one but I don’t recall how to do this, and it would be good to know what went wrong with the old page.
What went wrong was the last two lines:
Lecture Notes:
* D. A. Edwards and H. M. Hastings, _Čech and Steenrod Homotopy Theory with Applications,_ SLNM 542, Springer (1976).
*
That final *
confused Maruku as it was expecting a list item but got the end of the page. The smoke error was probably a bit drastic, though! (I’ve reported this to Jacques).
For “old hands”, it’s useful to know that even if the show
method is causing smoke, it’s still possible to manually get to the edit or source views simply by editing the URL. Sometimes there’s something really obviously wrong and changing it fixes the problem.
I see that Igor had also fixed a couple of wikilinks, so I’ve copied his version to proper homotopy theory, and I’ll blank (or almost blank) the new one and rename it to proper homotopy theory > history.
Incidentally, I don’t know why it suddenly started causing the bug. I do know that Jacques has been working on the maruku rendering engine to speed it up a little bit, so presumably it sneaked in there.
1 to 13 of 13