New naturally reductive spaces constructed with group isometries.
problem Creating new naturally reductive spaces.
method Constructing infinitesimal models, specifying transitive groups of isometries, and explicitly defining the naturally reductive structure.
result A large number of new naturally reductive spaces constructed.
Paper constructs naturally reductive spaces with a general formula.
problem Understanding naturally reductive spaces.
method Explicit construction from \cite{Storm2018} and general formula derivation.
result Proves reducibility and isomorphism criteria.
Constructs differential forms on C∞-ringed spaces.
problem Developing a theory of differential forms for non-manifold spaces.
method Functorial construction of differential forms on local C∞-ringed spaces. result Stokes' theorem holds for integrated forms on simplices.
We construct several non-trivial examples of CAT(1) spaces by using the idea of free construction.
New gauge-theoretic construction of 4D hyperkähler ALE spaces.
problem Classifying and understanding 4D hyperkähler ALE spaces.
method Gauge-theoretic construction of 4D hyperkähler ALE spaces via solutions to a system of equations for a pair of a connection and a section of a vector bundle over an orbifold Riemann surface, modulo a gauge group action.
result A new gauge-theoretic interpretation of Kronheimer's classification of 4D hyperkähler ALE spaces.
In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analyt…
We sharpen the construction of representation space in the paper "Principal Series Representations of Infinite Dimensional Lie Groups II: Construction of Induced Representations". We show that the principal series representation spaces constructed there, are completions of spaces of sections of Hilbert bundles rather t…
Authors construct parallel transport for tangent cones in Wasserstein space.
problem Parallel transport in tangent cones of Wasserstein space.
method Construction of parallel transport for tangent cones in the interior of a geodesic in Wasserstein space, proving linear part and extending to full tangent cones.
result The constructed parallel transport is equivalent to previous methods.
This work continues the study of a homotopy-theoretic construction of the author inspired by the Bott-Taubes integrals. Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots. Their techniques were later used by Cattaneo et al. to construct real…
Develops a finite construction for self-duality and related moduli spaces over Riemann surfaces.
problem Constructing moduli spaces over Riemann surfaces.
method Finite-dimensional construction using holomorphic symplectic reduction.
result Moduli spaces over Riemann surfaces as stratified holomorphic symplectic spaces.
Survey on gluing constructions under lower curvature bounds.
problem Understanding lower curvature bounds in various geometric contexts.
method Analyzes gluing constructions in smooth and non-smooth settings.
result Provides conjectures and theorems on synthetic lower Ricci curvature bounds.
Constructs a combinatorial model for bordered Riemann surfaces with a compactification.
problem Moduli spaces of bordered Riemann surfaces.
method Symmetric metric ribbon graphs and sequences of non-contractible subgraphs.
result A combinatorial moduli space that compactifies the KSV-compactification.
Constructs Nöbeling manifolds of arbitrary weight for any cardinal κ.
problem Creating Nöbeling manifolds of arbitrary weight for any cardinal κ.
method Constructs a space ν^n_κ(K) and a map π such that ν^n_κ(K) is a complete metric n-dimensional space of weight κ.
result Constructs Nöbeling manifolds of arbitrary weight for any cardinal κ.
The paper constructs hypersurfaces in symmetric space products.
problem Creating curvature-adapted hypersurfaces in symmetric space products.
method Constructing hypersurfaces using the product of symmetric spaces.
result Obtained many examples of curvature-adapted hypersurfaces.
We describe a construction (the `warped cone construction') which produces examples of coarse spaces with large groups of translations. We show that by this construction we can obtain many examples of coarse spaces which do not have property A or which are not uniformly embeddable into Hilbert space.
Constructs examples of centrally harmonic spaces and shows they are not generically harmonic.
problem Understanding conditions for centrally harmonic spaces.
method Generalizing work of Copson and Ruse to construct examples.
result Examples of centrally harmonic spaces are not generically harmonic.
We explicitly construct the twistor spaces of Joyce metrics with torus action that are not treated in Part I (math.DG/0603242). This finishes a construction of all the twistor spaces of Joyce metrics on the connected sum of four complex projective planes.
Covering space theory is used to construct new examples of buildings.
Constructs moduli spaces for monopoles with arbitrary symmetry breaking.
problem Finding moduli spaces for monopoles with varying symmetry.
method Defined configuration space with asymptotic conditions, performed quotient construction, used b-calculus and scattering calculus.
result Constructs hyper-Kähler moduli spaces for monopoles with arbitrary symmetry breaking.
In 1995 D. Joyce explicitly constructed a series of self-dual metrics with torus action on the connected sums of complex projective planes. In this paper we explicitly construct the twistor spaces of some of Joyce's self-dual metrics. Starting from a fiber space whose fibers are compact singular toric surfaces, we appl…
Constructs orthogonal coordinates in curved spaces.
problem Separating variables in curved spaces.
method Explicit construction of orthogonal coordinates and transformations.
result Explicit formulas for Killing tensors and Stäckel matrices.
Method constructs orthogonal curvilinear coordinates in constant curvature spaces.
problem Creating orthogonal coordinates in spaces of constant curvature.
method Modification of Krichever's method for Euclidean space, applied to constant curvature spaces.
result Examples of orthogonal coordinate systems on the sphere and hyperbolic plane constructed.
Paper constructs infinitely many tangent functors on diffeological spaces.
problem Tangent spaces in diffeological spaces are not uniquely defined.
method Introduced and constructed infinitely many non-isomorphic tangent functors.
result The choice of tangent functor is not unique outside smooth manifolds.
We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an elementary way by using associative algebras with several involutions. This constructi…
New proof for discrete Morse theory using combinatorial construction.
problem Verifying the Morse differential in discrete Morse homology.
method Combinatorial construction of flowlines in discrete Morse theory.
result Morse differential squares to zero in discrete Morse homology.
Simple construction for classifying spaces of projections of immersions.
problem Classifying spaces for projections of immersions with controlled singularities.
method Explicit simple construction for classifying spaces of maps obtained as hyperplane projections of immersions.
result Structure theorems for these classifying spaces.
The paper constructs coronas for combable spaces under specific conditions.
problem Constructing boundaries for combable spaces.
method Introducing properness, coherence, and expandingness for combings; constructing coronas using Rips complexes.
result Bijectivity of transgression maps, injectivity of the coarse assembly map, and surjectivity of the coarse co-assembly map for groups.
Isometric embeddings of Teichmüller spaces are derived from branched coverings.
problem Characterizing isometric embeddings of Teichmüller spaces.
method Holomorphic isometric embeddings induced by branched coverings.
result All isometric embeddings of Teichmüller spaces of dimension at least 2 arise from branched coverings.
We construct a C-space associated with every closed 3-form on a spacetime M and show that it depends on the class of the form in H3(M,Z). We also demonstrate that C-spaces have a relation to generalized geometry and to gerbes. C-spaces are constructed after introducing additional coordinates at the open sets and …
Constructs moduli space for discs mapping to homogeneous spaces.
problem Stable holomorphic discs mapping to homogeneous spaces.
method Orbifold with corners, fibered products, pushforward, pullback of differential forms.
result Moduli space of stable holomorphic discs as an orbifold with corners.
Geodesic orbit metrics proven on specific homogeneous spaces.
problem Geodesic orbit metrics on homogeneous spaces.
method Using strongly isotropy irreducible spaces and proving natural reductivity.
result Geodesic orbit metrics are naturally reductive on constructed homogeneous spaces.
Constructs retractions of CAT(1) spaces to convex subsets.
problem Geometric description of an analytic tool.
method Gradient flow of time-dependent locally Lipschitz semiconcave functions.
result Existence of gradient flows proved for independent interest.
Witt spaces are pseudomanifolds for which the middle-perversity intersection homology with rational coefficients is self-dual. We give a new construction of the symmetric signature for Witt spaces which is similar in spirit to the construction given by Miscenko for manifolds. Our construction has all of the expected pr…
We describe a construction of fibrewise inner products on the cotangent bundle of the smooth free loop space of a Riemannian manifold. Using this inner product, we construct an operator over the loop space of a string manifold which is directly analogous to the Dirac operator of a spin manifold.
New domains of discontinuity found for Anosov representations.
problem Understanding Anosov representations acting on homogeneous spaces.
method Constructing open domains of discontinuity for Anosov representations acting on specific homogeneous spaces.
result Describes the largest possible open domains of discontinuity for Zariski dense Anosov representations.
A bundle gerbe is constructed from an oriented smooth vector bundle of even rank with a fiberwise inner product, over a compact connected orientable smooth manifold with Riemannian metric. From a trivialization of the bundle gerbe is constructed an irreducible Clifford module bundle, a spinor bundle over the smooth fre…
Method to create rational Seifert surfaces for knots in Lens space.
problem Creating rational Seifert surfaces for knots in Lens space.
method Assuming a regular projection, construct rational Seifert surface on twist toroidal diagram.
result A method to construct rational Seifert surfaces for knots in Lens space.
New examples of structures found using twistor space.
problem Finding non-trivial generalized paracomplex structures.
method Twistor space construction scheme.
result Non-trivial examples of generalized paracomplex structures constructed.
New Brownian motion defined in Minkowski normed spaces.
problem Constructing Brownian motion in non-Euclidean spaces.
method Singular McKean--Vlasov stochastic differential equation.
result Pathwise uniqueness of solutions to the stochastic differential equation.
This paper constructs a non-Archimedean Teichmüller space using tropical geometry.
problem Constructing a non-Archimedean analogue of Teichmüller space.
method Using techniques from tropical and logarithmic geometry.
result The skeleton of non-Archimedean Teichmüller space is the tropical Teichmüller space.
The paper constructs compact λ-torus in Euclidean spaces.
problem Creating compact embedded λ-hypersurfaces with torus topology. method Constructing compact embedded λ-hypersurfaces with specific topology. result Compact embedded λ-torus in Euclidean spaces Rn+1 constructed. Constructs correspondences on hyperelliptic surfaces combining orbifold groups and Blaschke products.
problem Combining geometric and dynamical properties on hyperelliptic surfaces.
method Analytic combinations on Riemann sphere, algebraic characterization, and Teichmüller spaces.
result Explicit description of correspondences and injection into Hurwitz spaces.
The article constructs Spin(7) metrics with Aloff--Wallach spaces as orbits.
problem Creating Spin(7) metrics with specific geometric properties.
method Continuous 1-parameter families of non-compact Spin(7) metrics with chiralities, focusing on Aloff--Wallach spaces.
result Construction of Spin(7) metrics with Aloff--Wallach spaces as principal orbits, including geometric transitions.
The paper proves a theorem about constructing Higgs bundle moduli space.
problem Constructing the moduli space of Higgs bundles on a closed Riemann surface.
method Uses Kuranishi slice method and GIT quotient to prove the moduli space is a complex space locally modeled on a quadratic cone.
result The moduli space of Higgs bundles is a complex space locally modeled on an affine GIT quotient of a quadratic cone.
Method constructs Bryant surfaces in hyperbolic space.
problem Constructing Bryant type surfaces in hyperbolic space.
method Bianchi-Calo type construction method
result Constructs Bryant type surfaces in hyperbolic space.
The paper explores the complexities of algorithmic fairness and the assumptions needed for different fairness mechanisms.
problem The lack of a unified understanding of algorithmic fairness across different papers.
method Introducing a mathematical framework that includes the observed space, decision space, and construct space to analyze fairness mechanisms.
result Different fairness mechanisms require different assumptions about the relationship between unobservable variables (construct space) and observable variables (observed space).
Cluster structures on moduli spaces are linked to Legendrian knots.
problem Constructing cluster structures on moduli spaces.
method Quantization of exact Lagrangian fillings corresponding to Legendrian knots.
result Cluster structures can be deduced from Legendrian knots.
Paper constructs a new type of hypersurface in Euclidean spaces.
problem None explicitly stated; focuses on new hypersurface construction.
method Constructs an immersed, non-embedded Sn λ-hypersurface. result Constructs a new type of hypersurface in Euclidean spaces.