Geodesic
Isometric embeddings of surfaces for scl
Alexis Marchand1 orcid
1University of Cambridge, UK
Groups, geometry, and dynamics, Tome 19 (2025) no. 4, pp. 1445-1478

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DOI

Let φ:F1​→F2​ be an injective morphism of free groups. If φ is geometric (i.e., induced by an inclusion of oriented compact connected surfaces with nonempty boundary), then we show that φ is an isometric embedding for stable commutator length. More generally, we show that if T is a subsurface of an oriented compact (possibly closed) connected surface S, and c is an integral 1-chain on π1​T, then there is an isometric embedding H2​(T,c)→H2​(S,c) for the relative Gromov seminorm. Those statements are proved by finding an appropriate standard form for admissible surfaces and showing that, under the right homology vanishing conditions, such an admissible surface in S for a chain in T is in fact an admissible surface in T.
DOI : 10.4171/ggd/845
Classification : 20F65, 20J05, 57M07
Mots-clés : stable commutator length, relative Gromov seminorm, surfaces, isometric embeddings, rationality

Alexis Marchand  1

1 University of Cambridge, UK 
Alexis Marchand. Isometric embeddings of surfaces for scl. Groups, geometry, and dynamics, Tome 19 (2025) no. 4, pp. 1445-1478. doi: 10.4171/ggd/845
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