Open Access
Translator Disclaimer
2009 Intersections and joins of free groups
Richard Peabody Kent
Algebr. Geom. Topol. 9(1): 305-325 (2009). DOI: 10.2140/agt.2009.9.305

Abstract

Let H and K be subgroups of a free group of ranks h and kh, respectively. We prove the following strong form of Burns’ inequality:

rank(HK)12(h1)(k1)(h1)rank(HK)1.

A corollary of this, also obtained by L Louder and D B McReynolds, has been used by M Culler and P Shalen to obtain information regarding the volumes of hyperbolic 3–manifolds.

We also prove the following particular case of the Hanna Neumann Conjecture, which has also been obtained by Louder. If HK has rank at least (h+k+1)2, then HK has rank no more than (h1)(k1)+1.

Citation

Download Citation

Richard Peabody Kent. "Intersections and joins of free groups." Algebr. Geom. Topol. 9 (1) 305 - 325, 2009. https://doi.org/10.2140/agt.2009.9.305

Information

Received: 31 January 2008; Revised: 18 August 2008; Accepted: 28 January 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1170.20017
MathSciNet: MR2482079
Digital Object Identifier: 10.2140/agt.2009.9.305

Subjects:
Primary: 20E05
Secondary: 57M50

Rights: Copyright © 2009 Mathematical Sciences Publishers

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.9 • No. 1 • 2009
MSP
Back to Top