Translator Disclaimer
15 July 2017 Approximation by subgroups of finite index and the Hanna Neumann conjecture
Andrei Jaikin-Zapirain
Duke Math. J. 166(10): 1955-1987 (15 July 2017). DOI: 10.1215/00127094-0000015X

Abstract

Let F be a free group (pro-p group), and let U and W be two finitely generated subgroups (closed subgroups) of F. The Strengthened Hanna Neumann conjecture says that

xU\F/Wrk¯(UxWx1)rk¯(U)rk¯(W),whererk¯(U)=max {rk(U)1,0}. 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-p context, and we present a new proof in the abstract case. We also show that the Lück approximation conjecture holds for free groups.

Citation

Download Citation

Andrei Jaikin-Zapirain. "Approximation by subgroups of finite index and the Hanna Neumann conjecture." Duke Math. J. 166 (10) 1955 - 1987, 15 July 2017. https://doi.org/10.1215/00127094-0000015X

Information

Received: 29 November 2015; Revised: 17 November 2016; Published: 15 July 2017
First available in Project Euclid: 16 March 2017

zbMATH: 1375.20035
MathSciNet: MR3679885
Digital Object Identifier: 10.1215/00127094-0000015X

Subjects:
Primary: 20E18
Secondary: 16A06, 20C07, 20E05, 20J05, 22D25

Rights: Copyright © 2017 Duke University Press

JOURNAL ARTICLE
33 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.166 • No. 10 • 15 July 2017
Back to Top