Unsolvability of the isomorphism problem for [free abelian]-by-free groups

The isomorphism problem for [free abelian]-by-free groups is unsolvable.Comment: added reference to a paper by Bruno Zimmermann containing a similar result for (free abelian)-by-surface group

The Truth About Voter Fraud

Allegations of election-related fraud make for enticing press. Many Americans remember vivid stories of voting improprieties in Chicagoland, or the suspiciously sudden appearance of LBJ's alphabetized ballot box in Texas, or Governor Earl Long's quip: "When I die, I want to be buried in Louisiana, so I can stay active in politics." Voter fraud, in particular, has the feel of a bank heist caper: roundly condemned but technically fascinating, and sufficiently lurid to grab and hold headlines. Perhaps because these stories are dramatic, voter fraud makes a popular scapegoat. In the aftermath of a close election, losing candidates are often quick to blame voter fraud for the results. Legislators cite voter fraud as justification for various new restrictions on the exercise of the franchise. And pundits trot out the same few anecdotes time and again as proof that a wave of fraud is imminent.Allegations of widespread voter fraud, however, often prove greatly exaggerated. It is easy to grab headlines with a lurid claim ("Tens of thousands may be voting illegally!"); the follow-up -- when any exists -- is not usually deemed newsworthy. Yet on closer examination, many of the claims of voter fraud amount to a great deal of smoke without much fire. The allegations simply do not pan out

Characterizing rigid simplicial actions on trees

We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms preserving the set of elliptic subgroups).Comment: Geometric methods in group theory (2004) to appea

Counting growth types of automorphisms of free groups

Given an automorphism of a free group $F_n$, we consider the following invariants: $e$ is the number of exponential strata (an upper bound for the number of different exponential growth rates of conjugacy classes); $d$ is the maximal degree of polynomial growth of conjugacy classes; $R$ is the rank of the fixed subgroup. We determine precisely which triples $(e,d,R)$ may be realized by an automorphism of $F_n$. In particular, the inequality e\le (3n-2)/4} (due to Levitt-Lustig) always holds. In an appendix, we show that any conjugacy class grows like a polynomial times an exponential under iteration of the automorphism.Comment: final version, to appear in GAFA; proof of 3.1 simplified thanks to the refere

Quotients and subgroups of Baumslag-Solitar groups

We determine all generalized Baumslag-Solitar groups (finitely generated groups acting on a tree with all stabilizers infinite cyclic) which are quotients of a given Baumslag-Solitar group BS(m,n), and (when BS(m,n) is not Hopfian) which of them also admit BS(m,n) as a quotient. We determine for which values of r,s one may embed BS(r,s) into a given BS(m,n), and we characterize finitely generated groups which embed into some BS(n,n).Comment: Final version, to appear in Journal of Group Theor