Let S be a \(P^2\) -knot which is the connected sum of a 2-knot with normal Euler number 0 and an unknotted \(P^2\) -knot with normal Euler number \({\pm }{2}\) in a closed 4-manifold X with trisection \(T_{X}\) . Then, we show that the trisection of X obtained by the trivial gluing of relative trisections of \(\overline{\nu (S)}\) and \(X-\nu (S)\) is diffeomorphic to a stabilization of \(T_{X}\) . It should be noted that this result is not obvious since boundary-stabilizations introduced by Kim and Miller are used to construct a relative trisection of \(X-\nu (S)\) . As a corollary, if \(X=S^4\) and \(T_X\) was the genus 0 trisection of \(S^4\) , the resulting trisection is diffeomorphic to a stabilization of the genus 0 trisection of \(S^4\) . This result is related to the conjecture that is a 4-dimensional analogue of Waldhausen’s theorem on Heegaard splittings.
