Volume 21, issue 2 (2021)

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

Volume 24, 1 issue

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Moduli spaces of Hecke modifications for rational and elliptic curves

David Boozer

Algebraic & Geometric Topology 21 (2021) 543–600
Abstract

We propose definitions of complex manifolds 𝒫M(X,m,n) that could potentially be used to construct the symplectic Khovanov homology of n–stranded links in lens spaces. The manifolds 𝒫M(X,m,n) are defined as moduli spaces of Hecke modifications of rank 2 parabolic bundles over an elliptic curve X. To characterize these spaces, we describe all possible Hecke modifications of all possible rank 2 vector bundles over X, and we use these results to define a canonical open embedding of 𝒫M(X,m,n) into Ms(X,m + n), the moduli space of stable rank 2 parabolic bundles over X with trivial determinant bundle and m + n marked points. We explicitly compute 𝒫M(X,1,n) for n = 0,1,2. For comparison, we present analogous results for the case of rational curves, for which a corresponding complex manifold 𝒫M(1,3,n) is isomorphic for n even to a space 𝒴(S2,n) defined by Seidel and Smith that can be used to compute the symplectic Khovanov homology of n–stranded links in S3.

PDF Access Denied

We have not been able to recognize your IP address 3.129.39.55 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:

Keywords
Hecke modifications, rational curves, elliptic curves, vector bundles, parabolic bundles, Khovanov homology
Mathematical Subject Classification 2010
Primary: 14H52, 14H99
References
Publication
Received: 6 July 2018
Revised: 28 April 2020
Accepted: 1 June 2020
Published: 25 April 2021
Authors
David Boozer
Department of Mathematics
Princeton University
Princeton, NJ
United States