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# Recovering topological spaces from their auto-homeomorphism groups.

Vendredi, 22 Septembre, 2006 - 16:00
Prénom de l'orateur :
Matti
Nom de l'orateur :
RUBIN
Résumé :

Given two topological spaces $X$ and $Y$ we ask whether any algebraic isomorphism $phi$ between the homeomorphism groups $H(X)$ and $H(Y )$ of $X$ and $Y$ is a conjugation by some homeomorphism between $X$ and $Y$. That is, we ask whether there is $\tau : X \cong Y$ such that $\phi(g) = \tau \circ g \circ \tau^{1}$ for all $g \in H(X)$. I shall survey the work and open questions in this area. The following theorem will be explained.

Theorem: Let $X$ and $Y$ be open subsets of locally convex metrizable
topological vector spaces $E$ and $F$ respectively and $phi$ be an isomorphism between $H(X)$ and $H(Y)$. Then there is a homeomorphism $\tau$ between $X$ and $Y$ such that $\phi(g) = \tau \circ g \circ \tau^{1}$ for every $g \in H(X)$.

Institution de l'orateur :
Ben Gurion University, Tel Aviv
Thème de recherche :
Topologie
Salle :
04