arXiv research

Extends geometric decompositions to arbitrary meshes and forms.

The paper studies asymptotic dimensions of manifolds and spaces, proving key results about their geometric decompositions.

Study the structure of equidistant decompositions in manifolds.

New $f$-vectors reveal geometric Lefschetz-like decompositions of flag spheres.

Study decomposes geometric surfaces, finding special curves.

We present an algebraic investigation of generalized and equiaffine curvature tensors in a given pseudo-Euclidean vector space and study different orthogonal, irreducible decompositions in analogy to the known decomposition of algebraic curvature tensors. We apply the decomposition results to characterize geometric pro…

The paper explores geometric decompositions for Ricci tensors and their applications.

These notes are intended to be an introduction to the use of approximately holomorphic techniques in almost contact and contact geometry. We develop the setup of the approximately holomorphic geometry. Once done, we sketch the existence of the two main geometric decompositions available for an almost contact or contact…

Classifies Morse boundaries of 3-manifold groups.

The study proves properties of 4D projective manifolds and builds non-hyperbolic examples.

We construct a general approach to decomposition of the tangent bundle of pseudo-Riemannian manifolds into direct sums of subbundles, and the associated decomposition of geometric objects. An invariant structure {\cal H}^r defined as a set of r projection operators is used to induce decomposition of the geometric objec…

We show any Weyl curvature model can be geometrically realized by a Weyl manifold

This paper uses combinatorial Ricci flow to tackle Thurston's triangulation conjecture.

In this paper an extended CPR decomposition theorem for Finsler symmetric spaces of semi-negative curvature in the context of reductive structures is proven. This decomposition theorem is applied to give a geometric description of the complexification of some infinite dimensional homogeneous spaces.

Geometrically studies Moore-Penrose inverse and polar decomposition continuity.

Develops methods to analyze feature-outcome associations in subpopulations.

The study provides a structure theorem for a new class of noncompact 3-manifolds.

In this paper, we study face vectors of simplicial posets that are the face posets of cell decompositions of topological manifolds without boundary. We characterize all possible face vectors of simplicial posets whose geometric realizations are homeomorphic to the product of spheres. As a corollary, we obtain the chara…

Rational maps structure theorem with geometric decomposition and realizability proof.

Geometrically decomposes Kähler functions on toric manifolds.

The paper describes handle decompositions and Kirby diagrams for plane algebraic curves.

Geometrically describes hyperbolic structures on link complements using quantum groups.

We introduce Fenchel-Nielsen coordinates on Teicmüller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type can be turned into a geom…

Paper bounds tensor decomposition's RLCT, aiding Bayesian inference.

The paper describes decompositions of geometric measures on Anosov homogeneous spaces.

GETF efficiently decomposes large-scale Boolean tensors.

We study canonical decompositions of postcritically finite branched coverings of the 2-sphere, as defined by K. Pilgrim. We show that every hyperbolic cycle in the decomposition does not have a Thurston obstruction. It is thus Thurston equivalent to a rational map.

CDFD analyzes circularity and directionality in weighted directed networks.

In this paper, we determine the canonical polyhedral decomposition of every hyperbolic once-punctured torus bundle over the circle. In fact, we show that the only ideal polyhedral decomposition that is straight in the hyperbolic structure and that is invariant under a certain involution is the ideal triangulation defin…

We present an algorithm to construct the JSJ decomposition of one-ended hyperbolic groups which are fundamental groups of graphs of free groups with cyclic edge groups. Our algorithm runs in double exponential time, and is the first algorithm on JSJ decompositions to have an explicit time bound. Our methods are combina…

Decomposes flows with jumps into simpler components.

Strongly-cyclic branched coverings of knots are studied by using their (g,1)-decompositions. Necessary and sufficient conditions for the existence and uniqueness of such coverings are obtained. It is also shown that their fundamental groups admit geometric g-words cyclic presentations.

Study examines heart and football-shaped metrics, verifying geometric structure.

Constructs a simplicial cell decomposition of complex projective space for n ≥ 2.

Decompositions on manifolds appear in various geometric structures. Necessary and sufficient conditions for quotient spaces of decompositions to be manifolds are widely characterized. We characterize necessary and sufficient conditions to be $k$-manifolds $(k = 1, 2)$, which generalize characterizations in the codimens…

Geometric analysis on real analytic manifolds using seminorms.

This is the first in a series of four papers (with research announcement posted on this arXiv) that together develop a decomposition theory for subgroups of Out(F_n). In this paper we develop further the theory of geometric EG strata of relative train track maps originally introduced in the work of Bestvina, Feighn, an…

The space of probability densities is an infinite-dimensional Riemannian manifold, with Riemannian metrics in two flavors: Wasserstein and Fisher--Rao. The former is pivotal in optimal mass transport (OMT), whereas the latter occurs in information geometry---the differential geometric approach to statistics. The Rieman…

We show vanishing results about the infimum of the topological entropy of the geodesic flow of homogeneous smooth four manifolds. We prove that any closed oriented geometric four manifold has zero minimal entropy if and only if it has zero simplicial volume. We also show that if a four manifold M admits a geometric dec…

Decomposition complexity for metric spaces was recently introduced by Guentner, Tessera, and Yu as a natural generalization of asymptotic dimension. We prove a vanishing result for the continuously controlled algebraic K-theory of bounded geometry metric spaces with finite decomposition complexity. This leads to a proo…

The paper characterizes harmonic maps and studies their properties on Riemannian manifolds.

We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian manifold. This requires extending the Tricerri-Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen …

Researchers decompose Forman-Ricci curvature for efficient computation in VR complexes.

This paper solves a problem in 3D geometry by defining a canonical partition for certain manifolds.

We try to understand the geometric properties of $n$-manifolds ($n\geq 2$) with geometric structures modeled on $(\bR P^n, \PGL(n+1, \bR))$, i.e., $n$-manifolds with projectively flat torsion free affine connections. We define the notion of $i$-convexity of such manifolds due to Carriére for integers $i$, $1 \leq i \le…

Study of sectorial decompositions in symmetric products of surfaces for symplectic geometry.

The abstract proves spherical surface decompositions with conical singularities.

The purpose of this paper is to describe certain natural 4-vector fields on quaternionic flag manifolds, which geometrically determine the Bruhat cell decomposition. This structure naturally descends from the symplectic group, where it is related to the dressing action given by the Iwasawa decomposition of the general …