On-device research index

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·4 papers on “homology” in Geometric Topology · 1 month

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 ↗

Filling 1-cycles, 2-cycle complexity, and torsion growthmath.GT

Study 2-complexes' homology properties and torsion growth.

problem Quantitative connections between 1-cycle filling inequalities and homology complexities.

method Geometric lower bounds on first homology of finite covers.

result Geometric lower bound on first homology size of finite covers.

homology 2-complexes filling inequalities torsion growth property (τ)

2026-07-15abs ↗pdf ↗

Homological Topological Quantum Field Theoriesmath.GT

New framework for quantum invariants of 3-manifolds using homology.

problem Quantum invariants of 3-manifolds.

method Homological construction of mapping class group representations extended to cobordisms.

result Construction of a

(2+1)

-dimensional TQFT assigning twisted homology to surfaces.

quantum invariants 3-manifolds topological quantum field theory homology mapping class group

2026-07-10abs ↗pdf ↗

Torsion in the homology of the Torelli group and the Birman-Craggs-Johnson homomorphismmath.GT

The paper extends Johnson's result on Torelli group homology.

problem Understanding the homology of the Torelli group and its subgroups.

method Analyzing the pushforward homomorphism on higher homology groups induced by Dehn twists.

result The pushforward homomorphism is injective for certain subgroups of higher homology groups.

Torelli group homology Dehn twists Boolean polynomials injective homomorphism

2026-07-02abs ↗pdf ↗