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
The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups. We resolve these conjectures in the two generator case. More generally, we prove that every two-generator one-relator group with every infinite-index subgroup free is itself either free or a surface group.
Related project(s):
60Property (T)
We introduce the classes of TAP groups, in which various types of algebraic fibring are detected by the non-vanishing of twisted Alexander polynomials. We show that finitely presented LERF groups lie in the class TAP1(R) for every integral domain R, and deduce that algebraic fibring is a profinite property for such groups. We offer stronger results for algebraic fibring of products of limit groups, as well as applications to profinite rigidity of Poincaré duality groups in dimension 3 and RFRS groups.
Related project(s):
60Property (T)
We introduce the notion of quasi-BNS invariants, where we replace homomorphism to R by homogenous quasimorphisms to R in the theory of Bieri-Neumann-Strebel invariants. We prove that the quasi-BNS invariant QΣ(G) of a finitely generated group G is open; we connect it to approximate finite generation of almost kernels of homogenous quasimorphisms; finally we prove a Sikorav-style theorem connecting QΣ(G) to the vanishing of the suitably defined Novikov homology.
Related project(s):
60Property (T)
We provide a direct connection between the Zmax (or essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic two-generator one-relator group with abelianisation of rank 2.
We deduce various structural and algorithmic properties, like the existence of a quadratic-time algorithm computing the Zmax-JSJ decomposition of such groups.
Related project(s):
60Property (T)
We initiate the study of torsion-free algebraically hyperbolic groups; these groups generalise, and are intricately related to, groups with no Baumslag-Solitar subgroups. Indeed, for groups of cohomological dimension 2 we prove that algebraic hyperbolicity is equivalent to containing no Baumslag-Solitar subgroups. This links algebraically hyperbolic groups to two famous questions of Gromov; recent work has shown these questions to have negative answers in general, but they remain open for groups of cohomological dimension 2.
We also prove that algebraically hyperbolic groups are CSA, and so have canonical abelian JSJ-decompositions. In the two-generated case we give a precise description of the form of these decompositions.
Related project(s):
60Property (T)
We prove that twisted ℓ2-Betti numbers of locally indicable groups are equal to the usual ℓ2-Betti numbers rescaled by the dimension of the twisting representation; this answers a question of Lück for this class of groups. It also leads to two formulae: given a fibration E with base space B having locally indicable fundamental group, and with a simply-connected fibre F, the first formula bounds ℓ2-Betti numbers b(2)i(E) of E in terms of ℓ2-Betti numbers of B and usual Betti numbers of F; the second formula computes b(2)i(E) exactly in terms of the same data, provided that F is a high-dimensional sphere.
We also present an inequality between twisted Alexander and Thurston norms for free-by-cyclic groups and 3-manifolds. The technical tools we use come from the theory of generalised agrarian invariants, whose study we initiate in this paper.
Related project(s):
60Property (T)
We construct a new type of expanders, from measure-preserving affine actions with spectral gap on origami surfaces, in each genus g⩾1. These actions are the first examples of actions with spectral gap on surfaces of genus g>1. We prove that the new expanders are coarsely distinct from the classical expanders obtained via the Laplacian as Cayley graphs of finite quotients of a group. In genus g=1, this implies that the Margulis expander, and hence the Gabber--Galil expander, is coarsely distinct from the Selberg expander. For the proof, we use the concept of piecewise asymptotic dimension and show a coarse rigidity result: A coarse embedding of either R2 or H2 into either R2 or H2 is a quasi-isometry.
Related project(s):
60Property (T)