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Let $\varphi:F_1\to F_2$ be an injective morphism of free groups. If$\varphi$ is geometric (i.e. induced by an inclusion of oriented compactconnected surfaces with nonempty boundary), then we show that $\varphi$ is anisometric embedding for stable commutator length. More generally, we show thatif $T$ is a subsurface of an oriented compact (possibly closed) connectedsurface $S$, and $c$ is an integral $1$-chain on $\pi_1T$, then there is anisometric embedding $H_2(T,c)\to H_2(S,c)$ for the relative Gromov seminorm.Those statements are proved by finding an appropriate standard form foradmissible surfaces and showing that, under the right homology vanishingconditions, such an admissible surface in $S$ for a chain in $T$ is in fact anadmissible surface in $T$.

Isometric embeddings of surfaces for scl