New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education

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
 SEARCH THIS BOOK:
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

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.