Duke Mathematical Journal
- Duke Math. J.
- Volume 166, Number 10 (2017), 1955-1987.
Approximation by subgroups of finite index and the Hanna Neumann conjecture
Let be a free group (pro- group), and let and be two finitely generated subgroups (closed subgroups) of . The Strengthened Hanna Neumann conjecture says that
This conjecture was proved independently in the case of abstract groups by J. Friedman and I. Mineyev in 2011.
In this paper we give the proof of the conjecture in the pro- context, and we present a new proof in the abstract case. We also show that the Lück approximation conjecture holds for free groups.
Duke Math. J., Volume 166, Number 10 (2017), 1955-1987.
Received: 29 November 2015
Revised: 17 November 2016
First available in Project Euclid: 16 March 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20E18: Limits, profinite groups
Secondary: 20E05: Free nonabelian groups 20J05: Homological methods in group theory 16A06 20C07: Group rings of infinite groups and their modules [See also 16S34] 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]
Jaikin-Zapirain, Andrei. Approximation by subgroups of finite index and the Hanna Neumann conjecture. Duke Math. J. 166 (2017), no. 10, 1955--1987. doi:10.1215/00127094-0000015X. https://projecteuclid.org/euclid.dmj/1489629612