Isometric endomorphisms of free groups

  title={Isometric endomorphisms of free groups},
  author={Danny Calegari and Alden K. Walker},
An arbitrary homomorphism between groups is nonincreasing for stable commutator length, and there are infinitely many (injective) homomorphisms between free groups which strictly decrease the stable commutator length of some elements. However, we show in this paper that a random homomorphism between free groups is almost surely an isometry for stable commutator length for every element; in particular, the unit ball in the scl norm of a free group admits an enormous number of exotic isometries… CONTINUE READING

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