2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99820The 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.25 pages, revised version, to appear in J. Algebraic GeomAlgebraic Geometry14H60 (Primary) 14H10 (Secondary)text