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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.

169,341 papers · 148 categories

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8 results for “Four-torus”

Topology of holomorphic Lefschetz pencils on the four-torusmath.GT

The paper studies Lefschetz pencils on four-torus, proving their uniqueness and constructing examples.

problem Understanding the topology of Lefschetz pencils on the four-torus.

method Using moduli spaces of polarized abelian surfaces, the authors prove the uniqueness of pencils and construct examples.

result Holomorphic Lefschetz pencils on the four-torus are uniquely determined by their genus and divisibility.

Lefschetz pencils Four-torus Topology Holomorphic Abelian surfaces

2016-03-28abs ↗pdf ↗

Nonlinear Hodge flows in symplectic geometrymath.DG

The paper tackles isotropy of symplectic forms using Hodge flows.

problem Whether symplectic forms in a given class are isotropic.

method Introduces nonlinear Hodge heat flows to study isotropy.

result The flow converges to the symplectic form

ω

smoothly for any initial symplectic form in the class.

symplectic geometry Hodge flows isotropy four torus K3 surface

2023-10-05abs ↗pdf ↗

On the Scalar Curvature for the Noncommutative Four Torusmath.QA

The scalar curvature for the noncommutative four torus $\mathbb{T}_Θ^4$ , where its flat geometry is conformally perturbed by a Weyl factor, is computed by making the use of a noncommutative residue that involves integration over the 3-sphere. This method is more convenient since it does not require the rearrangement le…

2014-10-31abs ↗pdf ↗

Einstein-Hilbert Action and on the Gauss-Bonnet Theorem for Riemannian Noncommutative Torimath.DG

Study shows non-positivity of Einstein-Hilbert action for certain metrics.

problem Analyzing the non-positivity of the Einstein-Hilbert action for specific metrics.

method Using spectral triples and modular operator computations.

result Recovery of earlier results on noncommutative tori and new Gauss-Bonnet theorem.

Einstein-Hilbert action noncommutative tori spectral triples Gauss-Bonnet theorem non-diagonal metrics

2017-07-15abs ↗pdf ↗

Free torus actions and twisted suspensionsmath.GT

The paper classifies manifolds with free torus actions and positive Ricci curvature.

problem Classifying manifolds with specific geometric properties.

method Using circle bundles and free torus actions on connected sums of products of spheres.

result Infinitely-many manifolds with positive Ricci curvature and torus actions are classified.

torus actions positive Ricci curvature circle bundles closed manifolds

2023-05-10abs ↗pdf ↗

Toric geometry of Spin(7)-manifoldsmath.DG

Study $\mathrm{Spin}(7)$ -manifolds with a 4-torus action using a symmetric matrix ansatz.

problem Characterize

\mathrm{Spin}(7)

-manifolds with a 4-torus action.

method Provide a Gibbons-Hawking type ansatz using a symmetric

4 imes4

-matrix of functions.

result First known

\mathrm{Spin}(7)

-manifolds with a rank 4 symmetry group and full holonomy.

Spin(7)-manifolds 4-torus action Gibbons-Hawking ansatz symmetric matrix multi-Hamiltonian action

2018-10-30abs ↗pdf ↗

Nearly Parallel

\mathrm{G}_{2}

-Structures with Torus Symmetrymath.DG

Study nearly parallel G2-structures with torus symmetry using multi-moment maps.

problem Characterize and construct nearly parallel G2-structures with torus symmetry.

method Use multi-moment map techniques and analyze the geometry of the base spaces.

result Locally, the construction may produce examples with four-torus symmetry.

G2-structures torus symmetry multi-moment map Riemannian metric closed two-forms

2025-08-29abs ↗pdf ↗

On integral rigidity in Seiberg-Witten theorymath.GT

We prove integral rigidity for Seiberg-Witten invariants of 4-manifolds with specific hypersurfaces.

problem Integral rigidity of Seiberg-Witten invariants in 4-manifolds with non-separating hypersurfaces.

method Floer theoretic conditions and interplay between irreducible and reducible solutions to Seiberg-Witten equations.

result Sum of Seiberg-Witten invariants is determined cohomologically for specific 4-manifolds.

Seiberg-Witten invariants Floer homology integral rigidity 4-manifolds non-separating hypersurfaces

2024-09-26abs ↗pdf ↗