Instanton Floer homology with Lagrangian boundary conditions

DOI10.2140/gt.2008.12.747zbMath1166.57018arXivmath/0607318OpenAlexW1968703968WikidataQ63285636 ScholiaQ63285636MaRDI QIDQ2426849

Dietmar A. Salamon, Katrin Wehrheim

Publication date: 14 May 2008

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607318

zbMATH Keywords

3-manifold with boundaryAtiyah-Floer conjecture

Mathematics Subject Classification ID

Floer homology (57R58) Boundary value problems on manifolds (58J32)

Related Items

Seifert hypersurfaces of 2-knots and Chern-Simons functional, 4-Manifold topology, Donaldson–Witten theory, Floer homology and higher gauge theory methods in the BV-BFV formalism, Instantons for 4-manifolds with periodic ends and an obstruction to embeddings of 3-manifolds, Hadamard-type formulas via the Maslov form, The Morse and Maslov indices for Schrödinger operators, \(L^2\)-topology and Lagrangians in the space of connections over a Riemann surface, A compactness theorem for \(SO(3)\) anti-self-dual equation with translation symmetry, The correspondence induced on the pillowcase by the earring tangle, Floer cohomology and geometric composition of Lagrangian correspondences, Equivariant Lagrangian Floer homology via cotangent bundles of EGN$EG_N$, Morse homology for the Yang-Mills gradient flow, Self-adjoint curl operators, Atiyah-Floer conjecture: A formulation, a strategy of proof and generalizations, On the Fredholm Lagrangian Grassmannian, spectral flow and ODEs in Hilbert spaces, The Maslov index and the spectra of second order elliptic operators, Categorification of invariants in gauge theory and symplectic geometry, The Morse and Maslov indices for multidimensional Schrödinger operators with matrix-valued potentials, Floer Field Philosophy, Elliptic Yang–Mills flow theory, Floer theory and its topological applications

Cites Work

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• \(L^2\)-topology and Lagrangians in the space of connections over a Riemann surface
• Lagrangian boundary conditions for anti-self-dual instantons and the Atiyah-Floer conjecture
• Casson's invariant and gauge theory
• The moduli space of regular stable maps
• Theorems and problems in functional analysis. Transl. from the Russian by Harold H. McFaden
• Connections with \(L^ p \)bounds on curvature
• The Maslov index: A functional analytical definition and the spectral flow formula
• The Maslov index for paths
• Self-dual instantons and holomorphic curves
• Uhlenbeck compactness
• The orientation of Yang-Mills moduli spaces and 4-manifold topology
• An instanton-invariant for 3-manifolds
• Unique continuation theorems in gauge theories
• Four-manifold invariants from higher-rank bundles
• General spectral flow formula for fixed maximal domain
• Anti-self-Dual instantons with Lagrangian boundary conditions. I: Elliptic theory
• Anti-self-dual instantons with Lagrangian boundary conditions. II: Bubbling
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Spectral asymmetry and Riemannian Geometry. I
• The [eta-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary]
• The Yang-Mills equations over Riemann surfaces
• The Spectral Flow and the Maslov Index
• BANACH SPACE VALUED CAUCHY–RIEMANN EQUATIONS WITH TOTALLY REAL BOUNDARY CONDITIONS
• Lower Bounds and Uniqueness Theorems for Solutions of Differential Equations in a Hilbert Space