English

An index relation for the quilted Atiyah-Floer conjecture

Symplectic Geometry 2019-08-09 v4

Abstract

Given a closed, connected, oriented 3-manifold with positive first Betti number, one can define an instanton Floer group as well as a quilted Lagrangian Floer group. Each of these is equipped with a chain level grading. We show that the gradings agree.

Cite

@article{arxiv.1311.4004,
  title  = {An index relation for the quilted Atiyah-Floer conjecture},
  author = {David L. Duncan},
  journal= {arXiv preprint arXiv:1311.4004},
  year   = {2019}
}

Comments

The proof of Proposition 3.5 contains an error that the author has not yet been able to fix (this is due to an issue in the sibling paper [8]). As such, the results of this paper should be considered as conjectural until the gap is fixed. For more details, see the red comments in the previous version posted to arXiv

R2 v1 2026-06-22T02:08:39.871Z