Transversality via gauge transformations for pseudo holomorphic disks in projectivized vector bundles

Abstract

We show that one can achieve transversality for lifts of holomorphic disks to a projectivized vector bundle by locally enlarging the structure group and considering the action of gauge transformations on the almost complex structure, which eases computation considerably. As an application we prove a special case of the Arnold-Givental conjecture.

24 pages, 1 figure