AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane
Fabian Ziltener, Korea Institute for Advanced Study, Seoul, Republic of Korea

Memoirs of the American Mathematical Society
2014; 129 pp; softcover
Volume: 230
ISBN-10: 0-8218-9472-2
ISBN-13: 978-0-8218-9472-9
List Price: US$76
Individual Members: US$45.60
Institutional Members: US$60.80
Order Code: MEMO/230/1082
[Add Item]

Request Permissions

Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold \((M,\omega)\). Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten theory of \((M,\omega)\) to the Gromov-Witten theory of the symplectic quotient. The morphism should be a deformation of the Kirwan map. The idea, due to D. A. Salamon, is to define such a deformation by counting gauge equivalence classes of symplectic vortices over the complex plane \(\mathbb{C}\).

The present memoir is part of a project whose goal is to make this definition rigorous. Its main results deal with the symplectically aspherical case.

Table of Contents

  • Motivation and main results
  • Bubbling for vortices over the plane
  • Fredholm theory for vortices over the plane
  • Appendix A. Auxiliary results about vortices, weighted spaces, and other topics
  • Bibliography
Powered by MathJax

  AMS Home | Comments:
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia