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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·6 papers on “fundamental group” in Geometric Topology · 1 month

A combinatorial approach to obstructing left-orderability of Dehn fillingsmath.GT

New property helps show many knot fillings are not left-orderable.

problem Non-left-orderability of knot groups after Dehn filling.

method Introducing conjugate-slope property to study knot groups.

result The conjugate-slope property implies non-left-orderability of many knot fillings.

knot theory Dehn filling left-orderability fundamental group meridian

2026-07-17abs ↗pdf ↗

Knotted surfaces with simply-connected complementsmath.GT

Study knotted surfaces in simply-connected 4-manifolds with trivial boundary.

problem Locally flat, compact, genus g surfaces with boundary a fixed knot in simply-connected 4-manifolds with boundary the 3-sphere.

method Analyzes homology and isotopy of surfaces with trivial fundamental group complements.

result Homologous surfaces are topologically ambiently isotopic rel. boundary.

knot theory 4-manifolds fundamental group ambient isotopy homology

2026-07-16abs ↗pdf ↗

Symplectically aspherical Kähler manifolds, scalar curvature, and the fundamental groupmath.GT

Study symplectically aspherical Kähler manifolds with unique properties.

problem Existence and properties of symplectically aspherical Kähler manifolds.

method Detailed study and analysis of geometric and topological features.

result Existence of symplectically aspherical Kähler manifolds with large fundamental groups.

symplectically aspherical Kähler manifolds fundamental group scalar curvature Kähler forms universal cover

2026-07-06abs ↗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 ↗

PD_4

-complexes with

π_2

a projective

\mathbb{Z}[π_1]

-modulemath.GT

The paper classifies PD_4-complexes based on their fundamental group properties.

problem Understanding the structure of PD_4-complexes based on their fundamental group properties.

method Analyzing the fundamental group and its modules to classify PD_4-complexes.

result The classification of PD_4-complexes based on their fundamental group properties.

PD_4-complexes fundamental group projective modules torsion-free free product

2026-06-28abs ↗pdf ↗

On quasi-holomorphic homotopies of immersions of 3-manifolds into 5-manifoldsmath.GT

Quasi-holomorphic homotopies of immersions of 3-manifolds into 5-manifolds

problem The study of homotopies of immersions of 3-manifolds into 5-manifolds

method Describing the local form of quasi-holomorphic homotopies and connections with holomorphic map germs

result A complete description of how the fundamental group of the complement of the image of an immersion changes under a quasi-holomorphic homotopy

immersions homotopies fundamental group knot group holomorphic map germs

2026-06-25abs ↗pdf ↗