State-sum invariants of knotted curves and surfaces from quandle cohomology

Abstract

State-sum invariants for classical knots and knotted surfaces in 4-space are developed via the cohomology theory of quandles. Cohomology groups of quandles are computed to evaluate the invariants. Some twist spun torus knots are shown to be noninvertible using the invariants. © 1999 American Mathematical Society.