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Suppose M is a non-compact connected smooth n-manifold. Let D(M) denote thegroup of diffeomorphisms of M endowed with the compact-open C^\infty-topologyand D^c(M) denote the subgroup consisting of diffeomorphisms of M with compactsupport. Let D(M)_0 and D^c(M)_0 be the connected components of id_M in D(M)and D^c(M) respectively. In this paper we show that the pair (D(M), D^c(M))admits a topological (\prod^\omega \ell_2, \sum^\omega \ell_2)-factor. In thecase n = 2, this enables us to apply the characterization of (\prod^\omega\ell_2, \sum^\omega \ell_2)-manifolds and show that the pair (D(M)_0, D^c(M)_0)is a (\prod^\omega \ell_2, \sum^\omega \ell_2)-manifold and determine itstopological type. We also obtain a similar result for groups of homeomorphismsof non-compact topological 2-manifolds.

Topological (\prod^\omega \ell_2, \sum^\omega \ell_2)-factors of diffeomorphism groups of non-compact manifolds