On homeomorphism groups of non-compact surfaces, endowed with the Whitney topology

TL;DR

This paper characterizes the topological structure of the homeomorphism group of non-compact surfaces with the Whitney topology, showing it is homeomorphic to a product of well-known infinite-dimensional spaces.

Contribution

It provides a complete topological classification of the homeomorphism groups of non-compact surfaces with the Whitney topology, identifying their homeomorphism types.

Findings

Homeomorphism groups are homeomorphic to R^∞×l_2 or Z×R^∞×l_2.

The topology of these groups is explicitly characterized.

The results apply to all non-compact connected surfaces.

Abstract

We prove that for any non-compact connected surface $M$ the group $H_c(M)$ of compactly suported homeomorphisms of $M$ endowed with the Whitney topology is homeomorphic to $R^\infty\times l_2$ or $Z\times R^\infty\times l_2$.