English

Equivariant, string and leading order characteristic classes associated to fibrations

Mathematical Physics 2015-08-03 v4 Differential Geometry math.MP

Abstract

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 S^1 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.

Keywords

Cite

@article{arxiv.1309.2692,
  title  = {Equivariant, string and leading order characteristic classes associated to fibrations},
  author = {Andres Larrain-Hubach and Yoshiaki Maeda and Steven Rosenberg and Fabian Torres-Ardila},
  journal= {arXiv preprint arXiv:1309.2692},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-22T01:24:36.267Z