Abelian covers of graphs and maps between outer automorphism groups of free groups

Details Abelian covers of graphs and maps between outer automorphism groups of free groups Abelian covers of graphs and maps between outer automorphism groups of free groups

2010-07-15

arxiv.org/abs/1007.2598v3

Mathematics

Group Theory

Final version, to appear in Mathematische Annalen. Minor errors and typos corrected, including range of n in Theorem B

Scientific paper

We explore the existence of homomorphisms between outer automorphism groups of free groups Out(F_n) \to Out(F_m). We prove that if n > 8 is even and n \neq m \leq 2n, or n is odd and n \neq m \leq 2n - 2, then all such homomorphisms have finite image; in fact they factor through det: Out(F_n) \to Z/2. In contrast, if m = r^n(n - 1) + 1 with r coprime to (n - 1), then there exists an embedding Out(F_n) \to Out(F_m). In order to prove this last statement, we determine when the action of Out(F_n) by homotopy equivalences on a graph of genus n can be lifted to an action on a normal covering with abelian Galois group.

Affiliated with

Also associated with

No associations

Rating

Abelian covers of graphs and maps between outer automorphism groups of free groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Abelian covers of graphs and maps between outer automorphism groups of free groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Abelian covers of graphs and maps between outer automorphism groups of free groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-599652