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.

168,695 papers · 148 categories

Trend · papers per month

count % of corpus

7 results for “Sigma-invariants”

On some manifolds with positive sigma invariants and their realizing conformal classesmath.DG

The study proves properties of metrics and their conformal classes on specific manifolds.

problem Understanding metrics and their conformal classes on certain manifolds.

method Combining Simons' gap theorem with minimal isometric embeddings and coherent embeddings of standard Einstein metrics.

result The conformal classes of the product metrics and projective spaces realize the sigma invariant uniquely.

metrics conformal classes sigma invariant minimal embeddings Riemannian products

2023-11-09abs ↗pdf ↗

Sigma-invariants and tropical varietiesmath.AG

BNSR invariants are contained in the complement of tropical varieties.

problem Understanding the relationship between algebraic and topological invariants.

method Showed containment of BNSR invariants in the complement of tropical varieties.

result BNSR invariants are contained in the complement of tropical varieties.

Sigma-invariants tropical varieties Novikov-Sikorav homology Bieri-Neumann-Strebel-Renz invariants characteristic varieties

2020-10-15abs ↗pdf ↗

On the slice genus of linksmath.GT

We define Casson-Gordon sigma-invariants for links and give a lower bound of the slice genus of a link in terms of these invariants. We study as an example a family of two component links of genus h and show that their slice genus is h, whereas the Murasugi-Tristram inequality does not obstruct this link from bounding …

2003-11-09abs ↗pdf ↗

Closed manifolds, model geometries, and volume related differentiable invariantsmath.DG

The study classifies manifolds based on their geometric properties and invariants.

problem Classifying manifolds based on their geometric and topological properties.

method Analyzing metrics through isometric embeddings and deformations, considering scalar curvature, Ricci tensor, and Einstein metrics.

result The KW type classification of manifolds and sigma invariant calculations.

manifolds geometry invariants isometric embeddings scalar curvature

2026-07-14abs ↗pdf ↗

The sigma invariant of the

n

torus, the K3 surface, and Euclidean and elliptic 3d manifoldsmath.DG

The sigma invariant is studied for torus, K3 surface, and 3d manifolds.

problem Investigating the sigma invariant for specific manifolds.

method Analyzing isometric embeddings and scalar curvature functionals.

result Sigma invariant is zero for torus, K3 surface, and certain 3d manifolds.

sigma invariant torus K3 surface 3d manifolds isometric embeddings

2025-09-30abs ↗pdf ↗

Arithmetic group symmetry and finiteness properties of Torelli groupsmath.GR

We examine groups whose resonance varieties, characteristic varieties and Sigma-invariants have a natural arithmetic group symmetry, and we explore implications on various finiteness properties of subgroups. We compute resonance varieties, characteristic varieties and Alexander polynomials of Torelli groups, and we sho…

2010-02-03abs ↗pdf ↗

Conformal properties of spheresmath.DG

Identifies metrics on manifolds and their embeddings into spheres, characterizing constant curvature metrics.

problem Characterizing metrics on manifolds and their embeddings into spheres.

method Identifies metrics on manifolds and their embeddings into spheres, characterizes metrics of constant scalar curvature, and uses Yamabe metrics and almost Hermitian structures.

result Characterizes metrics of constant scalar curvature by properties of extrinsic quantities of their embeddings.

metrics embeddings spheres constant scalar curvature Yamabe metrics

2024-05-25abs ↗pdf ↗