Kirby--Thompson Invariants of Distant Sums of Standard Surfaces

Blair–Campisi–Taylor–Tomova BCTT22 defined the Formula: see text-invariant Formula: see text of a knotted surface Formula: see text, using pants complexes of trisection surfaces of bridge trisections of Formula: see text. After that, Aranda–Pongtanapaisan–Zhang APZ23 introduced the Formula: see text-invariant Formula: see text using dual curve complexes instead of pants complexes. In this paper, we determine both the Formula: see text-invariant and the Formula: see text-invariant of any finite distant sum of standard surfaces, and this is the first example of knotted surfaces whose bridge numbers and these invariants can be arbitrarily large.