We construct locally supported, continuous wavelets on manifolds G that
are given as the closure of a disjoint union of general smooth parametric images of an
n-simplex. The wavelets are proven to generate Riesz bases for Sobolev spaces Hs(G)
when s E (-1, 3/2 ), if not limited by the global smoothness of G. These results generalize
the findings from [DSt99], where it was assumed that each parametrization has a constant
Jacobian determinant. The wavelets can be arranged to satisfy the cancellation property of
in principal any order, except for wavelets with supports that extend to different patches,
which generally satisfy the cancellation property of only order 1
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