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