Title: Minimal surfaces in the 3-sphere by desingularizing intersecting Clifford tori,
Abstract: For each integer $k \geq 2$, we apply gluing methods to construct sequences
of minimal surfaces embedded in the round $3$-sphere. We produce two types of
sequences, all desingularizing collections of intersecting Clifford tori.
Sequences of the first type converge to a collection of $k$ Clifford tori
intersecting with maximal symmetry along these two circles. Near each of the
circles, after rescaling, the sequences converge smoothly on compact subsets to
a Karcher-Scherk tower of order $k$. Sequences of the second type desingularize
a collection of the same $k$ Clifford tori supplemented by an additional
Clifford torus equidistant from the original two circles of intersection, so
that the latter torus orthogonally intersects each of the former $k$ tori along
a pair of disjoint orthogonal circles, near which the corresponding rescaled
sequences converge to a singly periodic Scherk surface. The simpler examples of
the first type resemble surfaces constructed by Choe and Soret \cite{CS} by
different methods where the number of handles desingularizing each circle is
the same. There is a plethora of new examples which are more complicated and on
which the number of handles for the two circles differs. Examples of the second
type are new as well.