S. Gersten announced an algorithm that takes as input two finite sequences and of conjugacy classes of finitely generated subgroups of and outputs:
- (1) YES or NO depending on whether or not there is an element such that together with one such if it exists and
- (2) a finite presentation for the subgroup of fixing .
S. Kalajdžievski published a verification of this algorithm. We present a different algorithm from the point of view of Culler–Vogtmann’s Outer space. New results include that the subgroup of fixing is of type , an equivariant version of these results, an application, and a unified approach to such questions.
[FH19] The conjugacy problem for UPG elements of (2019) (https://arxiv.org/abs/1906.04147)
[Lev] McCool groups and stabilizers on the boundary of outer space (joint work with Vincent Guirardel, research announcement, http://people.maths.ox.ac.uk/drutu/conference/levitt.pdf)
[Vog17] Contractibility of outer space: reprise, Hyperbolic geometry and geometric group theory. Proceedings of the 7th Seasonal Institute of the Mathematical Society of Japan (MSJ-SI), Tokyo, Japan, July 30 – August 5, 2014 (Advanced Studies in Pure Mathematics), Volume 73, Mathematical Society of Japan, 2017, pp. 265-280 | DOI | MR | Zbl