Higher-rank instanton cohomology and the quilted Atiyah-Floer conjecture

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. The quilted Atiyah-Floer conjecture states that these cohomology groups are isomorphic. We initiate a program for proving this conjecture.

51 pages, 3 figures

References in corpus (5)

• Quilted Floer Cohomology
• On the components of the gauge group for PU(r)-bundles
• Compactness results for neck-stretching limits of instantons
• Four-manifold invariants from higher-rank bundles
• An index relation for the quilted Atiyah-Floer conjecture

Cited by in corpus (2)

• The pillowcase and traceless representations of knot groups II: a Lagrangian-Floer theory in the pillowcase
• An index relation for the quilted Atiyah-Floer conjecture