4 Citations
`2–TORSION OF FREE-BY-CYCLIC GROUPS
- Mathematics
- 2016
We provide an upper bound on the `2–torsion of a free-bycyclic group, −ρ(2)(F oΦ Z), in terms of a relative train-track representative for Φ ∈ Aut(F). Our result shares features with a theorem of…
The Bieri–Neumann–Strebel invariants via Newton polytopes
- MathematicsInventiones mathematicae
- 2019
We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather than formal…
Dynamics on free-by-cyclic groups
- Mathematics
- 2015
Given a free-by-cyclic group GD FN A’ Z determined by any outer automorphism ’2 Out.FN/ which is represented by an expanding irreducible train-track map f , we construct a K.G;1/ 2‐complex X called…
$\ell^{2}$-torsion of free-by-cyclic groups
- Mathematics
- 2015
We provide an upper bound on the $\ell^{2}$-torsion of a free-by-cyclic group, $-\rho^{(2)}(\mathbb{F} \rtimes_{\Phi} \mathbb{Z})$, in terms of a relative train-track representative for $\Phi \in…
References
SHOWING 1-10 OF 14 REFERENCES
The expansion factors of an outer automorphism and its inverse
- Mathematics
- 2004
A fully irreducible outer automorphism o of the free group F n of rank n has an expansion factor which often differs from the expansion factor of o -1 Nevertheless, we prove that the ratio between…
Parageometric outer automorphisms of free groups
- Mathematics
- 2004
We study those fully irreducible outer automorphisms o of a finite rank free group F r which are parageometric, meaning that the attracting fixed point of o in the boundary of outer space is a…
Dynamics on free-by-cyclic groups
- Mathematics
- 2015
Given a free-by-cyclic group GD FN A’ Z determined by any outer automorphism ’2 Out.FN/ which is represented by an expanding irreducible train-track map f , we construct a K.G;1/ 2‐complex X called…
Asymmetry of Outer space
- Mathematics
- 2009
We study the asymmetry of the Lipschitz metric d on Outer space. We introduce an (asymmetric) Finsler norm $${\|\cdot\|^L}$$ that induces d. There is an Out(Fn)-invariant “potential” Ψ defined on…
McMullen polynomials and Lipschitz flows for free-by-cyclic groups
- Mathematics
- 2013
Consider a group G and an epimorphism u_0:G\to\Z inducing a splitting of G as a semidirect product ker(u_0)\rtimes_\varphi\Z with ker(u_0) a finitely generated free group and \varphi\in Out(ker(u_0))…
MATH
- Biology
- 1992
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
2 ,
- Physics
- 1993
Since 2001, we have observed the central region of our Galaxy with the near-infrared (J, H, and Ks) camera SIRIUS and the 1.4 m telescope IRSF. Here I present the results about the infrared…
Leininger
- McMullen polynomials and Lipschitz flows for free-bycyclic groups.
- 2013