A note on invariants of flows induced by Abelian differentials on Riemann surfaces

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The real and imaginary part of any Abelian differential on a compact Riemann surface define two flows on the underlying compact orientable C∞ surface. Furthermore, these flows induce an interval exchange transformation on every transversal simple closed curve, via Poincaré recurrence. This note shows that the ordered K₀ groups of several C algebras naturally associated to one of the flows resp. interval exchange transformations are isomorphic, mainly using methods of I. Putnam.