DOIAbstract
AbstractLet M be a compact surface, χ(M)<0, and let Γ = π1M. Let S(M) be the set of isotopy classes of multiple simple loops on M. Each λ ϵ S(M) determines a family of cyclic words W = W(λ), with associated coinitial graph τ. The finite set of coinitial graphs, obtained as λ ranges over S(M), is interpreted as a set of ‘π1-train tracks’ on M. The linearity theorem asserts that if a topologically induced automorphism ø of Γ maps the set of weights W supported on τ to a set supported on τ′, then, with appropriate restrictions, the action is linear on the positive linear span of the W's
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