We define the stable –genus of a knot , , to be the limiting value of , where denotes the –genus and goes to infinity. This induces a seminorm on the rationalized knot concordance group, . Basic properties of are developed, as are examples focused on understanding the unit ball for on specified subspaces of . Subspaces spanned by torus knots are used to illustrate the distinction between the smooth and topological categories. A final example is given in which Casson–Gordon invariants are used to demonstrate that can be a noninteger.
"The stable $4$–genus of knots." Algebr. Geom. Topol. 10 (4) 2191 - 2202, 2010. https://doi.org/10.2140/agt.2010.10.2191