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

2013/11/21 by David L. Duncan, Duncan, David L. · 3 citations
Mathematics · #53D40 #57R58 #Advanced Combinatorial Mathematics #Betti number #Cohomology #Combinatorics #Conjecture #Differential Geometry (math.DG) #FOS: Mathematics #Floer homology #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Instanton #Mathematical physics #Mathematics #Pure mathematics #Rank (graph theory) #Symplectic Geometry (math.SG) #Symplectic geometry #math.DG #math.SG #msc:53D40 #msc:57R58

paper · pdf · doi:10.48550/arxiv.1311.5609

published in arXiv (Cornell University) (Cornell University) · 51 pages, 3 figures

openalex publication_date 2013/11/21 · arxiv created 2015/05/07 · arxiv updated 2015/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the components of the gauge group for PU(r)-bundles
• Four-manifold invariants from higher-rank bundles

Related

• An index relation for the quilted Atiyah-Floer conjecture
• Atiyah-Floer Conjecture: a Formulation, a Strategy to Prove and Generalizations
• Lagrangians, SO(3)-instantons and the Atiyah-Floer Conjecture
• Instanton Floer homology with Lagrangian boundary conditions
• Instanton Floer homology with Lagrangian boundary conditions