Publications of SPP2026
On this site you find preprints and publications produced within the projects and with the support of the DFG priority programme „Geometry at Infinity“.
- all projects
- 01Hitchin components for orbifolds
- 02Asymptotic geometry of sofic groups and manifolds
- 03Geometric operators on a class of manifolds with bounded geometry
- 04Secondary invariants for foliations
- 05Index theory on Lorentzian manifolds
- 06Spectral Analysis of Sub-Riemannian Structures
- 07Asymptotic geometry of moduli spaces of curves
- 08Parabolics and invariants
- 09Diffeomorphisms and the topology of positive scalar curvature
- 10Duality and the coarse assembly map
- 11Topological and equivariant rigidity in the presence of lower curvature bounds
- 12Anosov representations and Margulis spacetimes
- 13Analysis on spaces with fibred cusps
- 14Boundaries of acylindrically hyperbolic groups and applications
- 15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds
- 16Minimizer of the Willmore energy with prescribed rectangular conformal class
- 17Existence, regularity and uniqueness results of geometric variational problems
- 18Analytic L2-invariants of non-positively curved spaces
- 19Boundaries, Greens formulae and harmonic functions for graphs and Dirichlet spaces
- 20Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings
- 21Stability and instability of Einstein manifolds with prescribed asymptotic geometry
- 22Willmore functional and Lagrangian surfaces
- 23Spectral geometry, index theory and geometric flows on singular spaces
- 24Minimal surfaces in metric spaces
- 25The Willmore energy of degenerating surfaces and singularities of geometric flows
- 26Projective surfaces, Segre structures and the Hitchin component for PSL(n,R)
- 27Invariants and boundaries of spaces
- 28Rigidity, deformations and limits of maximal representations
- 29Curvature flows without singularities
- 30Nonlinear evolution equations on singular manifolds
- 31Solutions to Ricci flow whose scalar curvature is bounded in Lp.
- 32Asymptotic geometry of the Higgs bundle moduli space
- 33Gerbes in renormalization and quantization of infinite-dimensional moduli spaces
- 34Asymptotic geometry of sofic groups and manifolds II
- 35Geometric operators on singular domains
- 36Cohomogeneity, curvature, cohomology
- 37Boundary value problems and index theory on Riemannian and Lorentzian manifolds
- 38Geometry of surface homeomorphism groups
- 39Geometric invariants of discrete and locally compact groups
- 40Construction of Riemannian manifolds with scalar curvature constraints and applications to general relativity
- 41Geometrically defined asymptotic coordinates in general relativity
- 42Spin obstructions to metrics of positive scalar curvature on nonspin manifolds
- 43Singular Riemannian foliations and collapse
- 44Actions of mapping class groups and their subgroups
- 45Macroscopic invariants of manifolds
- 46Ricci flows for non-smooth spaces, monotonic quantities, and rigidity
- 47Self-adjointness of Laplace and Dirac operators on Lorentzian manifolds foliated by noncompact hypersurfaces
- 48Profinite and RFRS groups
- 49Analysis on spaces with fibred cusps II
- 50Probabilistic and spectral properties of weighted Riemannian manifolds with Kato bounded Bakry-Emery-Ricci curvature
- 51The geometry of locally symmetric manifolds via natural maps
- 52Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds II
- 53Gauge-theoretic methods in the geometry of G2-manifolds
- 54Cohomology of symmetric spaces as seen from infinity
- 55New hyperkähler spaces from the the self-duality equations
- 56Large genus limit of energy minimizing compact minimal surfaces in the 3-sphere
- 57Existence, regularity and uniqueness results of geometric variational problems II
- 58Profinite perspectives on l2-cohomology
- 59Laplacians, metrics and boundaries of simplicial complexes and Dirichlet spaces
- 60Property (T)
- 61At infinity of symmetric spaces
- 62A unified approach to Euclidean buildings and symmetric spaces of noncompact type
- 63Uniqueness in mean curvature flow
- 64Spectral geometry, index theory and geometric flows on singular spaces II
- 65Resonances for non-compact locally symmetric spaces
- 66Minimal surfaces in metric spaces II
- 67Asymptotics of singularities and deformations
- 68Minimal Lagrangian connections and related structures
- 69Wall-crossing and hyperkähler geometry of moduli spaces
- 70Spectral theory with non-unitary twists
- 71Rigidity, deformations and limits of maximal representations II
- 72Limits of invariants of translation surfaces
- 73Geometric Chern characters in p-adic equivariant K-theory
- 74Rigidity, stability and deformations in nearly parallel G2-geometry
- 75Solutions to Ricci flow whose scalar curvature is bounded in L^p II
- 76Singularities of the Lagrangian mean curvature flow
- 77Asymptotic geometry of the Higgs bundle moduli space II
- 78Duality and the coarse assembly map II
- 79Alexandrov geometry in the light of symmetry and topology
- 80Nonlocal boundary problems: Index theory and semiclassical asymptotics
This paper relates different approaches to the asymptotic geometry of the
Hitchin moduli space of SL(2,C) Higgs bundles on a closed Riemann surface and,
via the nonabelian Hodge theorem, the character variety of SL(2,C)
representations of a surface group. Specifically, we find an asymptotic
correspondence between the analytically defined limiting configuration of a
sequence of solutions to the self-duality equations constructed by
Mazzeo-Swoboda-Weiss-Witt, and the geometric topological shear-bend parameters
of equivariant pleated surfaces due to Bonahon and Thurston. The geometric link
comes from a study of high energy harmonic maps. As a consequence we prove: (1)
the local invariance of the partial compactification of the moduli space by
limiting configurations; (2) a refinement of the harmonic maps characterization
of the Morgan-Shalen compactification of the character variety; and (3) a
comparison between the family of complex projective structures defined by a
quadratic differential and the realizations of the corresponding flat
connections as Higgs bundles, as well as a determination of the asymptotic
shear-bend cocycle of Thurston's pleated surface.
Related project(s):
27Invariants and boundaries of spaces32Asymptotic geometry of the Higgs bundle moduli space
We develop an algebro-analytic framework for the systematic study of the continuous bounded cohomology of Lie groups in large degree. As an application, we examine the continuous bounded cohomology of PSL(2,R) with trivial real coefficients in all degrees greater than two. We prove a vanishing result for strongly reducible classes, thus providing further evidence for a conjecture of Monod. On the cochain level, our method yields explicit formulas for cohomological primitives of arbitrary bounded cocycles.
| Journal | Journal of Topology and Analysis |
| Link to preprint version | |
| Link to published version |
Related project(s):
27Invariants and boundaries of spaces
We present a new technique that employs partial differential equations in order to explicitly construct primitives in the continuous bounded cohomology of Lie groups. As an application, we prove a vanishing theorem for the continuous bounded cohomology of SL(2,R) in degree 4, establishing a special case of a conjecture of Monod.
| Journal | Geometry & Topology |
| Volume | 19 |
| Pages | 3603–3643 |
| Link to preprint version | |
| Link to published version |
Related project(s):
27Invariants and boundaries of spaces