Taras Banakh*
Akademia Swietokrzyska w Kielcach, Poland and Lviv National University, Ukraine
Homeomorphism groups of non-compact surfaces and graphs
It is shown that for any connected non-compact surface $X$ the connected component $H_0(X)$ of the homeomorphism group $H(X)$ of $X$, endowed with the Whitney (or graph) topology, is homeomorphic to $\mathbb R^\infty\times \ell_2$.
Also for any non-compact connected 1-dimensional CW-complex $X$ of density $\kappa$ the homeomorphism group $H(X)$ with the Whitney topology is homeomorphic to the $\kappa$-th power $(\ell_2)^\kappa$ of the separable Hilbert space $\ell_2$ endowed with the box-topology, while $H_0(X)$ is homeomorphic to the subspace $(\ell_2)^\kappa_0$ of $(\ell_2)^\kappa$ consisting of sequences $(x_\alpha)_{\alpha\kappa}$ with finite support $\{\alpha : x_\alpha\ne 0\}$.
* This is a joint work with K. Mine and K. Sakai.
