Yang-Mills theory over surfaces and the Atiyah-Segal theorem

DOI10.2140/agt.2008.8.2209zbMath1240.19005arXiv0710.0681OpenAlexW3104888305MaRDI QIDQ1007187

Daniel A. Ramras

Publication date: 20 March 2009

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

Full work available at URL: https://arxiv.org/abs/0710.0681

zbMATH Keywords

Morse theoryYang-Mills functionalunitary flat connectionsdeformation \(K\)-theoryAtiyah-Segal completion theoremaspherical surfacesHarder-Narasimhan stratification

Mathematics Subject Classification ID

Connective (K)-theory, cobordism (19L41) Moduli problems for differential geometric structures (58D27) Topological (K)-theory (55N15) Equivariant (K)-theory (19L47) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)

Related Items (11)

Bad representations and homotopy of character varieties ⋮ Periodicity in the stable representation theory of crystallographic groups ⋮ A finite-dimensional approach to the strong Novikov conjecture ⋮ Moduli spaces of vector bundles over a Klein surface ⋮ On the Yang–Mills stratification for surfaces ⋮ Fundamental groups of character varieties: surfaces and tori ⋮ Excision for deformation \(K\)-theory of free products ⋮ Smoothing maps into algebraic sets and spaces of flat connections ⋮ The homotopy groups of a homotopy group completion ⋮ The homotopy types of gauge groups of nonorientable surfaces and applications to moduli spaces ⋮ The stable moduli space of flat connections over a surface

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Construction of universal bundles. II
• Elementary structure of real algebraic varieties
• Characters and cohomology of finite groups
• The product formula in unitary deformation \(K\)-theory
• Yang-Mills connections on nonorientable surfaces
• The topology of discrete groups
• On the bundle of connections and the gauge orbit manifold in Yang-Mills theory
• Connections with \(L^ p \)bounds on curvature
• The topology of the space of stable bundles on a compact Riemann surface
• Homology fibrations and the 'group-completion' theorem
• On the cohomology groups of moduli spaces of vector bundles on curves
• Lie group valued moment maps
• Characters and \(K\)-theory of discrete groups
• A local analytic splitting of the holonomy map on flat connections
• An application of transversality to the topology of the moduli space of stable bundles
• Uhlenbeck compactness
• Linear embeddings of semialgebraic \(G\)-spaces
• Categories and cohomology theories
• A duality between string topology and the fusion product in equivariant \(K\)-theory
• Derived completions in stable homotopy theory
• Excision for deformation \(K\)-theory of free products
• Rings, modules, and algebras in infinite loop space theory
• Classifying spaces and spectral sequences
• Equivariant \(K\)-theory and completion
• On the Yang–Mills stratification for surfaces
• Derived representation theory and the algebraic K -theory of fields
• Compact Lie Groups
• On the Yang-Mills heat equation in two and three dimensions.
• On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces
• Symmetric spectra
• The Yang-Mills equations over Riemann surfaces
• Rational computations of the topological K-theory of classifying spaces of discrete groups
• A Finitely Generated Infinite Simple Group
• On approximation in real Banach spaces
• The completion theorem in \(K\)-theory for proper actions of a discrete group

This page was built for publication: Yang-Mills theory over surfaces and the Atiyah-Segal theorem