Volume 23, issue 4 (2019)

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

Volume 23
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Holomorphic curves in exploded manifolds: regularity

Brett Parker

Geometry & Topology 23 (2019) 1621–1690
Abstract

The category of exploded manifolds is an extension of the category of smooth manifolds; for exploded manifolds, some adiabatic limits appear as smooth families. This paper studies the ̄ equation on variations of a given family of curves in an exploded manifold. Roughly, we prove that the ̄ equation on variations of an exploded family of curves behaves as nicely as the ̄ equation on variations of a smooth family of smooth curves, even though exploded families of curves allow the development of normal-crossing or log-smooth singularities. The resulting regularity results are foundational to the author’s construction of Gromov–Witten invariants for exploded manifolds.

Keywords
holomorphic curves, exploded manifolds, regularity of dbar equation, gluing analysis
Mathematical Subject Classification 2010
Primary: 58J99
References
Publication
Received: 11 February 2011
Revised: 6 August 2018
Accepted: 22 October 2018
Published: 17 June 2019
Proposed: Tomasz Mrowka
Seconded: Peter Ozsváth, Dan Abramovich
Authors
Brett Parker
School of Mathematics
Monash University
Melbourne, VIC
Australia