From Hyperbolic Dehn Filling to Surgeries in Representation Varieties
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Publication:5055439
DOI10.1007/978-3-030-97560-9_6zbMath1506.57011arXiv2105.14948OpenAlexW3170150213MaRDI QIDQ5055439
Publication date: 13 December 2022
Published in: In the Tradition of Thurston II (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2105.14948
elliptic operatorHiggs bundlecharacter varietyparabolic structurehyperbolic Dehn surgeryhigher Teichmüller space
Moduli problems for differential geometric structures (58D27) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) General geometric structures on low-dimensional manifolds (57M50) Vector bundles on curves and their moduli (14H60) General topology of 3-manifolds (57K30)
Cites Work
- Higher laminations and affine buildings
- Ends of the moduli space of Higgs bundles
- The pressure metric for Anosov representations
- Theorie der Normalflächen. Ein Isotopiekriterium für den Kreisknoten
- Über das Homöomorphieproblem der 3-Mannigfaltigkeiten. I
- A representation of orientable combinatorial 3-manifolds
- Parabolic Higgs bundles and representations of the fundamental group of a punctured surface into a real group
- Higgs bundles and higher Teichmüller spaces
- An algorithm to decide if a 3-manifold is a Haken manifold
- Universal bounds for hyperbolic Dehn surgery
- Cross ratios and identities for higher Teichmüller-Thurston theory
- Cross ratios, surface groups, \(\text{PSL}(n,\mathbb R)\) and diffeomorphisms of the circle
- Geometric invariant theory and decorated principal bundles
- Surface group representations with maximal Toledo invariant
- Hitchin components and hyperconvex representations of surface groups
- The symplectic nature of fundamental groups of surfaces
- Fricke spaces
- Topological components of spaces of representations
- The Teichmüller theory of harmonic maps
- Flat G-bundles with canonical metrics
- Average bending of convex pleated planes in hyperbolic three-space
- Moduli of vector bundles on curves with parabolic structures
- Self-dual Yang-Mills connections on non-self-dual 4-manifolds
- Rational surgery calculus: Extension of Kirby's theorem
- The Fenchel-Nielsen deformation
- Infinite energy harmonic maps and degeneration of hyperbolic surfaces in moduli space
- Higgs bundles and local systems
- Lie groups and Teichmüller space
- On the first Betti number of a constant negatively curved manifold
- A calculus for framed links in \(S^3\)
- Construction of the moduli space of stable parabolic Higgs bundles on a Riemann surface
- Bounds on the average bending of the convex hull boundary of a Kleinian group
- The moduli space of hyperbolic cone structures
- Positivity and higher Teichmüller theory
- Moduli spaces of Higgs bundles on degenerating Riemann surfaces
- Topology of representation spaces of surface groups in \(\mathrm{PSL}_2(\mathbb R)\) with assigned boundary monodromy and nonzero Euler number
- Moduli for decorated tuples of sheaves and representation spaces for quivers
- On the Cappell-Lee-Miller gluing theorem.
- A non-Haken hyperbolic 3-manifold covered by a surface bundle
- Anosov representations: domains of discontinuity and applications.
- The maximal number of exceptional Dehn surgeries
- Geometrisation of 3-manifolds
- Basmajian-type inequalities for maximal representations
- Topological invariants of parabolic \(G\)-Higgs bundles
- \(\mathrm{SO}(p,q)\)-Higgs bundles and higher Teichmüller components
- Collar lemma for Hitchin representations
- On discrete subgroups of Lie groups. I, II
- Maximal representations, non-Archimedean Siegel spaces, and buildings
- Eigenvalues and entropy of a Hitchin representation
- Maximal representations of surface groups: symplectic Anosov structures
- Moduli spaces of local systems and higher Teichmüller theory
- Anosov flows, surface groups and curves in projective space
- On irreducible 3-manifolds which are sufficiently large
- Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces
- An introduction to pressure metrics for higher Teichmüller spaces
- Harmonic Bundles on Noncompact Curves
- The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
- A collar lemma for partially hyperconvex surface group representations
- SO(n, n+1)-surface group representations and Higgs bundles
- Foundations of Hyperbolic Manifolds
- Deformations of hyperbolic structures
- The Self-Duality Equations on a Riemann Surface
- Twisted Harmonic Maps and the Self-Duality Equations
- Constructing Variations of Hodge Structure Using Yang-Mills Theory and Applications to Uniformization
- Modifications and Cobounding Manifolds
- Moduli of vector bundles on curves with parabolic structures
- Wild non-abelian Hodge theory on curves
- A Gluing Construction for Periodic Monopoles
- Self-adjoint elliptic operators and manifold decompositions part I: Low Eigenmodes and stretching
- Topological invariants of Anosov representations
- Model Higgs bundles in exceptional components of the Sp(4, ℝ)-character variety
- A gluing theorem for the Kapustin–Witten equations with a Nahm pole
- Exposé Bourbaki 1159 : Higher rank Teichmüller theories
- AN INVITATION TO HIGHER TEICHMÜLLER THEORY
- Basmajian's identity in higher Teichmüller–Thurston theory
- Higgs bundles and surface group representations in the real symplectic group
- Bending in the space of quasi-Fuchsian structures
- Compact Riemann surfaces. An introduction to contemporary mathematics
- Components of spaces of representations and stable triples.
- McShane Identities for Higher Teichmüller Theory and the Goncharov–Shen Potential
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