Irreducibility of a free group endomorphism is a mapping torus invariant
نویسندگان
چکیده
We prove that the property of a free group endomorphism being irreducible is invariant ascending HNN extension it defines. This answers question posed by Dowdall-Kapovich-Leininger. further and atoroidal commensurability invariant. The invariance follows from an algebraic characterization extensions determines exactly when their defining endomorphisms are atoroidal; specifically, we show if only has no infinite index subgroups extensions.
منابع مشابه
The mapping torus group of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth
We prove that the mapping torus group Fn ⋊α Z of any automorphism α of a free group Fn of finite rank n ≥ 2 is weakly hyperbolic relative to the canonical (up to conjugation) family H(α) of subgroups of Fn which consists of (and contains representatives of all) conjugacy classes that grow polynomially under iteration of α. Furthermore, we show that Fn ⋊α Z is strongly hyperbolic relative to the...
متن کاملIrreducibility of a Symmetry Group Implies Isotropy
We derive minimal conditions on a symmetry group of a linearly elastic material that implies its isotropy. A natural setting for the formulation and analysis is provided by the group representation theory where the necessary and sufficient conditions for isotropy are expressed in terms of the irreducibility of certain group representations. We illustrate the abstract results by (re)deriving sev...
متن کاملA Ρ–invariant of Iterated Torus Knots
We compute ρ–invariant for iterated torus knots K for the standard representation π1(S \ K) → Z given by abelianisation. For algebraic knots, this invariant turns out to be very closely related to an invariant of a plane curve singularity, coming from algebraic geometry.
متن کاملAn Endomorphism of the Khovanov Invariant
We construct an endomorphism of the Khovanov invariant to prove H-thinness and pairing phenomena of the invariants for alternating links. As a consequence, it follows that the Khovanov invariant of an oriented nonsplit alternating link is determined by its Jones polynomial, signature, and the linking numbers of its components.
متن کاملInvariant Ideals of Abelian Group Algebras under the Torus Action of a Field, I
Let V = V1 ⊕ V2 be a finite-dimensional vector space over an infinite locally-finite field F . Then V admits the torus action of G = F • by defining (v1 ⊕ v2) = v1g−1 ⊕ v2g. If K is a field of characteristic different from that of F , then G acts on the group algebra K[V ] and it is an interesting problem to determine all G-stable ideals of this algebra. In this paper, we consider the special c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2021
ISSN: ['0010-2571', '1420-8946']
DOI: https://doi.org/10.4171/cmh/506