Approximating topological surfaces in $4$-manifolds
Approximating topological surfaces in $4$-manifolds
Let ${M^2}$ be a compact, connected $2$-manifold with $\partial {M^2} \ne \emptyset$ and let $h:{M^2} \to {W^4}$ be a topological embedding of ${M^2}$ into a $4$-manifold. The main theorem of this paper asserts that if ${W^4}$ is a piecewise linear $4$-manifold, then $h$ can be arbitrarily closely approximated by locally …