2002/10/25 by A Chiodo, Chiodo, Alessandro
Mathematics · #14H60 (Primary) 14H10 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0210398
openalex publication_date 2002/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.