Timeline for When do isometric actions exist?
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10 events
| when toggle format | what | by | license | comment | |
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| Mar 7, 2011 at 1:26 | comment | added | Theo Buehler | I'm sorry, you seem to be right. I'll correct this answer as soon as I have it figured out. | |
| Mar 4, 2011 at 7:35 | comment | added | Kamran Reihani | But we have $\delta_X(x,x)>0$. Am I missing something? | |
| Feb 28, 2011 at 8:41 | comment | added | Theo Buehler | Monod's thesis is where I learned about it from (Monod and I are students of Marc Burger and Monod was one of the co-examiners of my thesis) :) | |
| Feb 28, 2011 at 4:58 | comment | added | Kamran Reihani | I also learned from the book "Continuous bounded cohomology of locally compact groups" by Nicolas Monod (P. 44, Lemma 4.5.4) that the existence of the generalized Bruhat functions was explicitly stated in Bourbaki, "INTEGRATION", published in 1963. It is the Proposition 8 on p. 51 (French version). (I think Koszul lectures were published in 1965.) | |
| Feb 27, 2011 at 21:02 | comment | added | Theo Buehler | Thanks for the reference, good to know that! The formula as well as the construction of a Bruhat function is implicitly contained in Koszul's lectures, I think (at least it was a major source of inspiration for me). The main idea definitely goes back to Bruhat. I really prefer to think of Bruhat functions as sort of transverse partitions of unity. The extension to groupoids is (as usual) not so difficult, as soon as you have the case of transformation groups right (I found it myself when I was thinking about amenable groupoids some years ago). | |
| Feb 27, 2011 at 20:18 | comment | added | Kamran Reihani | Many thanks for the formula! I was just playing around with the sums of the Bruhat functions instead of their products. I was quite sure this was folklore, and I agree that it is hard to locate it in the literature. The term "cut-off" function, however, was used by Jean-Louis Tu in his paper "La conjecture de Novikov pour les feuilletages hyperboliques", published in 1999 in K-theory. He proved the existence of such a function in his Proposition 6.11 for any locally compact proper groupoid with Haar system. I couldn't find any earlier reference, though. He might be the first one publishing it. | |
| Feb 26, 2011 at 18:26 | history | edited | Theo Buehler | CC BY-SA 2.5 |
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| Feb 26, 2011 at 13:46 | history | edited | Theo Buehler | CC BY-SA 2.5 |
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| Feb 26, 2011 at 13:32 | history | edited | Theo Buehler | CC BY-SA 2.5 |
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| Feb 26, 2011 at 13:20 | history | answered | Theo Buehler | CC BY-SA 2.5 |