2013/09/30 by Andres Larrain-Hubach, Yoshiaki Maeda, Steven Rosenberg +1
Physics and Astronomy · Mathematics · #math-ph #math.DG #math.MP
paper · pdf · doi:10.1016/j.geomphys.2014.01.011
An error in Section 3 invalidates the main result in this section. The error is discussed in T. McCauley, "S^1-Equivariant Chern-Weil Constructions on Loop Spaces," arXiv:1507.08626
arxiv created 2015/07/31 · arxiv updated 2015/08/03
We construct equivariant, string and leading order characteristic classes and Chern-Simons classes for certain infinite rank bundles associated to fibrations occurring in loop spaces, Gromov-Witten theory and gauge theory. Results include a restatement of the S1 index theorem using equivariant classes on the tangent bundle to loop space; the expression of some GW invariants in terms of string and leading order classes for infinite rank bundles over moduli spaces of pseudoholomorphic curves for semipositive symplectic manifolds; the identification of the real cohomology of a loop group with certain string and leading order classes; the identification of Donaldson's nu-class for 4-manifolds with a leading order class for the fibration of irreducible connections A over the quotient A/G by the gauge group.