User rupert - MathOverflow

definition of a weakly doubly transitive group action

2013-05-22T07:57:34Z

I'm reading Francis M. Choucroun, "Analyse harmonique des groupes d'automorphismes d'arbres de Bruhat-Tits", Mémoires de la S. M. F., tome 58 (1994), p. 1 - 166, and he speaks of a weakly doubly transitive or weakly triply transitive group action (in French). My first thought was that maybe this means that the group acts transitively on the unordered pairs or unordered tripes, but when you actually look at the arguments involving the notion that interpretation seems not to be supported. I was wondering if anyone could clarify what the meaning of "weakly doubly transitive" is in this paper.

article by Jacques Tits about automorphism group of a locally finite tree

2012-09-20T08:56:41Z

I believe that there might be an article by Jacques Tits somewhere in which he shows that a locally finite tree can be recovered from the topological group structure on its automorphism group (with the compact-open topology). Because the vertices can be identified with maximal compact subgroups, and one can give a criterion for when two vertices are adjacent.

If anyone happens to know the reference for this I'd be very grateful.

orthogonal group over local field

2012-03-03T14:15:21Z

Would anyone be able to tell me how to prove that the orthogonal group over a local field for an anisotropic quadratic form is compact?

quadratic forms over fields of characteristic 2

2012-03-20T12:56:07Z

I was wondering if anyone knows any good sources for the theory of quadratic forms over fields of characteristic 2 which are written in English?

how to prove that localisation preserves Hom's

2012-03-13T13:54:11Z

Can anyone tell me where I can read a proof that the natural map

$Hom_{A}(M,N)[S^{-1}]\rightarrow Hom_{A[S^{-1}]}(M[S^{-1}],N[S^{-1}])$

is an isomorphism if $M$ is finitely presented?

Woodin cardinals and weakly homgeneous trees

2011-05-30T23:37:07Z

I am reading "The Stationary Tower" trying to understand the proof of Theorem 1.5.12: "If $\delta$ is a Woodin cardinal, $Z$ is a set, and $T$ is a tree on $\omega\times Z$, then there is an $\alpha<\delta$ such that the forcing Coll($\omega,\alpha$) makes $T$ $<\delta$-weakly homogeneous."

It starts by showing that we can assume without loss of generality that $|T|\geq\delta$. Then it says "Fix a regular cardinal $\eta>\delta$ with $T\in V_{\eta}$ and let $T^{*}$ be the subtree of $T$ consisting of all nodes definable in $V_{\eta}$ from $T, \delta$ and parameters in $V_{\delta}$... $T$ and $T^{*}$ have the same projection in any forcing extension by a partial order in $V_{\delta}$."

I can see that this would be true if the set $Z$ had a definable well-ordering because then given any finite sequence of natural numbers $s$ there would be a definable node in $T_{s}$. But I am not sure why it would be true in general.

Comment by Rupert

2013-01-11T12:48:22Z

I thank woodbass for pointing out the error in Theorem 3.1 of my thesis. I have been pondering these issues since he sent me that message, and I believe I have a modified statement which is true: namely, a map $RP^{n}\rightarrow RP^{n}$ preserving collineaity, whose image contains at least $n+2$ points any $n+1$ of which are in general position, is an element of $PGL(n,R)$. I hope to write up the proof of this soon. I also believe that I can answer the question originally posed in this thread in the affirmative. I will communicate with woodbass about this shortly.