English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Alexander and Thurston norms, and the Bieri-Neumann-Strebel invariants for free-by-cyclic groups

Funke, F., & Kielak, D. (2018). Alexander and Thurston norms, and the Bieri-Neumann-Strebel invariants for free-by-cyclic groups. Geometry & Topology, 22(5), 2647-2696. doi:10.2140/gt.2018.22.2647.

Item is

Files

show Files
hide Files
:
arXiv:1605.09067.pdf (Preprint), 436KB
Name:
arXiv:1605.09067.pdf
Description:
File downloaded from arXiv at 2019-05-27 13:55
OA-Status:
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
:
Funke-Kielak_Alexander and Thurston norms_2018.pdf (Publisher version), 575KB
 
File Permalink:
-
Name:
Funke-Kielak_Alexander and Thurston norms_2018.pdf
Description:
-
OA-Status:
Visibility:
Restricted (Max Planck Institute for Mathematics, MBMT; )
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show
hide
Locator:
http://dx.doi.org/10.2140/gt.2018.22.2647 (Publisher version)
Description:
-
OA-Status:

Creators

show
hide
 Creators:
Funke, Florian1, Author           
Kielak, Dawid, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

Content

show
hide
Free keywords: Mathematics, Group Theory, Geometric Topology
 Abstract: We investigate Friedl-Lück's universal $L^2$-torsion for descending HNN extensions of finitely generated free groups, and so in particular for
$F_n$-by-$\mathbb{Z}$ groups. This invariant induces a seminorm on the first
cohomology of the group which is an analogue of the Thurston norm for
$3$-manifold groups. We prove that this Thurston semi-norm is an upper bound
for the Alexander semi-norm defined by McMullen, as well as for the higher
Alexander seminorms defined by Harvey. The same inequalities are known to hold
for $3$-manifold groups. We also prove that the Newton polytopes of the universal $L^2$-torsion of a descending HNN extension of $F_2$ locally determine the Bieri-Neumann-Strebel invariant of the group. We give an explicit means of computing the BNS invariant for such groups. As a corollary, we prove that the Bieri-Neumann-Strebel invariant of a descending HNN extension of $F_2$
has finitely many connected components. When the HNN extension is taken over
$F_n$ along a polynomially growing automorphism with unipotent image in $GL(n,\mathbb{Z})$, we show that the Newton polytope of the universal $L^2$-torsion and the BNS invariant completely determine one another. We also show that in this case the Alexander norm, its higher incarnations, and the Thurston norm all coincide.

Details

show
hide
Language(s): eng - English
 Dates: 2018
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Geometry & Topology
  Abbreviation : Geom. Topol.
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 22 (5) Sequence Number: - Start / End Page: 2647 - 2696 Identifier: -