Gluing support $\tau$-tilting modules via symmetric ladders of height 2

Gluing techniques with respect to a recollement have long been studied. Recently, ladders of recollements of abelian categories were introduced as important tools. We present explicit constructions of gluing of support $\tau$-tilting modules via symmetric ladders of height two. Moreover, we apply the result to triangular matrix algebras to give a more detailed version of the known Jasso's reduction and study maximal green sequences.