  The Witten top Chern class is the crucial cohomology class needed to state a
conjecture by Witten relating the Gelfand-Dikii hierarchies to higher spin
curves. In math.AG/0011032, Polishchuk and Vaintrob provide an algebraic
construction of such a class. We present a more straightforward construction
via K-theory. In this way we short-circuit the passage through bivariant
intersection theory and the use of MacPherson's graph construction.
Furthermore, we show that the Witten top Chern class admits a natural lifting
to the K-theory ring.
