Volume 25, issue 6 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 27
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Braid monodromy of univariate fewnomials

Alexander Esterov and Lionel Lang

Geometry & Topology 25 (2021) 3053–3077

Let 𝒞d d+1 be the space of nonsingular, univariate polynomials of degree d. The Viète map 𝒱 : 𝒞d Symd() sends a polynomial to its unordered set of roots. It is a classical fact that the induced map 𝒱 at the level of fundamental groups realises an isomorphism between π1(𝒞d) and the Artin braid group Bd. For fewnomials, or equivalently for the intersection 𝒞 of 𝒞d with a collection of coordinate hyperplanes in d+1, the image of the map 𝒱: π1(𝒞) Bd is not known in general.

We show that the map 𝒱 is surjective provided that the support of the corresponding polynomials spans as an affine lattice. If the support spans a strict sublattice of index b, we show that the image of 𝒱 is the expected wreath product of b with Bdb. From these results, we derive an application to the computation of the braid monodromy for collections of univariate polynomials depending on a common set of parameters.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

braid group, monodromy, fewnomial, tropical geometry
Mathematical Subject Classification 2010
Primary: 20F36, 55R80, 14T05
Received: 19 February 2020
Revised: 6 July 2020
Accepted: 6 August 2020
Published: 30 November 2021
Proposed: Mladen Bestvina
Seconded: Jim Bryan, Benson Farb
Alexander Esterov
Faculty of Mathematics
HSE University
Lionel Lang
Department of Electrical Engineering, Mathematics and Science
University of Gävle