| Determining the minimal possible genus of a cobordism between algebraic knots has been a difficult and subtle problem which arises naturally from algebraic geometry and four-dimensional aspects of knot theory. This dissertation focuses on a particular case of this question, namely whether this minimal genus can realize an obvious lower bound. The main goal is to obtain a condition under which the lower bound cannot be reached. This goal is attained by calculating the first singularity of the Upsilon function, a recently defined invariant derived from Heegaard Floer homology, of an algebraic knot. In the calculation, the use of semigroups plays an important role. We also explore the behavior of semigroups under cabling operations. |
