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Results tagged with automorphism-groups
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user 1463
Questions about the group of automorphisms of any mathematical object $X$ endowed with a given structure, i.e the group of all bijective maps from $X$ to itself preserving this structure, and hence helping study it further and understand it better.
11
votes
Accepted
Automorphism group of a free product
This is not an answer, but it's too long for a comment and makes an important point that I hope is useful.
It's not enough to think of your group just as some free product. To understand its automorph …
- 25.2k
21
votes
Accepted
Does the injection $\text{Aut}(F_n) \hookrightarrow \text{Aut}(F_{n+1})$ split?
Bridson and Vogtmann proved a much stronger result. From the abstract: 'If $m$ is less than $n$ then [the image of] a homomorphism $\mathrm{Aut}(F_n)\to\mathrm{Aut}(F_m)$ can have cardinality at most …
- 25.2k
4
votes
Accepted
Is the conjugacy problem solvable in $Out(F_n)$?
One result in this direction is given by Dahmani . His algorithm will determine conjugacy for pairs of atoroidal outer automorphisms, ie automorphisms that do not fix a non-trivial conjugacy class. …
- 25.2k