claude

To a regular projection of a knot we associate a finite dimensional non-commutative associative algebra which is self-injective and special biserial.

Using Seiberg-Witten theory, it is shown that any Kaehler metric of constant negative scalar curvature on a compact 4-manifold M minimizes the L^2-norm of scalar curvature among Riemannian metrics compatible with a fixed decomposition H^2(M)=(H^+) + (H^-). This implies, for example, that any such metric on a minimal ruled surface must be locally symmetric.