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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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← all fields·7 papers on “topology” in Geometric Topology · 1 month

Sharp Weitzenböck and PIC2 Estimates from Sectional-Scalar Curvature Pinchingmath.DG

Sharp estimates link curvature to topology, proving manifold rigidity.

problem Proving rigidity of manifolds under curvature pinching conditions.

method Sharp pointwise estimates and normalized Ricci flow.

result Proves manifold rigidity under strict sectional-scalar curvature pinching.

curvature pinching topology rigidity normalized Ricci flow algebraic curvature tensor

2026-07-20abs ↗pdf ↗

Topology of the links of cDV singularities of types

cA_n

for

n>0

and

cD_n

for

n>4

math.GT

Study on homology groups of cDV singularity links, identifying their topology.

problem Identify the topology of links of cDV singularities of types

cA_n

and

cD_n

method Analyzing the second integral homology group of the links, using results from Smale and Thom-Sebastiani sums.

result The homology groups of the links are determined for cDV singularities of types

cA_n

and

cD_n

cDV singularities homology groups topology integral homology link

2026-07-12abs ↗pdf ↗

Topological line arrangements with high multiplicitiesmath.GT

Study on constraints for topological and smooth realizations of line arrangements and configurations.

problem Investigating constraints on topological and smooth realizations of combinatorial line arrangements and

(n_k)

-configurations.

method Exploring constraints via locally-flatly or smoothly embedded 2-spheres, using Furuta's 10/8-Theorem, and G-signature theorem.

result Established a new lower bound for

(n_k)

-configurations, showing

n \geq k^2-5

for topological realizations.

line arrangements configurations topology smoothness Hirzebruch's inequality

2026-07-10abs ↗pdf ↗

Locally Euclidean Discretized Graph Configuration Spacesmath.GT

Classifies graph configuration spaces homeomorphic to manifolds.

problem Classifying graph configuration spaces homeomorphic to manifolds.

method Developed techniques to translate topological properties into graph theoretic ones.

result Extended Abrams' work to classify certain graph configuration spaces.

graph configuration spaces manifolds topology graph theory discretization

2026-07-09abs ↗pdf ↗

Soft cells, Tubular Tilings and the Hidden Phases in Binary Mixturesphysics.app-ph

New method extracts hidden phases in binary mixtures using tubular tilings.

problem Hidden phases in binary mixtures are difficult to observe.

method Introduce tubular tilings for discretizing binary mixtures on smooth manifolds.

result Recover topological information about hidden phases from observable phases and interfaces.

binary mixtures tubular tilings hidden phases topology Euler balance laws

2026-07-07abs ↗pdf ↗

The topology of Schottky spaces in higher dimensionsmath.GT

In higher dimensions, Schottky spaces have unique topological properties.

problem Characterize the topology of Schottky spaces in higher dimensions.

method Analyzing the fundamental group and homotopy properties of Schottky spaces in the borderline dimension.

result In the borderline dimension, the space is simply connected but has a dense open part with fundamental group a product of cyclic groups of order two.

Schottky spaces higher dimensions fundamental group topology simply connected

2026-07-01abs ↗pdf ↗

Low-dimensional topology of deep neural networkscs.LG

We simplify neural networks to 3D to study their topological changes.

problem Understanding how neural network layers affect low-dimensional topological invariants.

method Limiting each layer to a width of 3D space, tracking changes in linking numbers.

result ResNets and transformers are equally powerful in changing linking numbers.

neural networks topology linking numbers ResNets transformers

2026-06-30abs ↗pdf ↗