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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.

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7 results for “singquandle”

Polynomial Invariants of Singular Knots and linksmath.GT

New polynomial invariant distinguishes singular links.

problem Distinguishing singular links using existing invariants.

method Generalized quandle polynomial to singquandles and constructed a singular link invariant.

result New polynomial invariant distinguishes singular links with same counting invariant.

singular knot singular link singquandle polynomial invariant quandle counting invariant

2020-10-26abs ↗pdf ↗

On the axioms of singquandlesmath.GT

New axioms for singquandles simplify applications and reveal algebraic aspects.

problem Axiomatizing singular knots and links.

method Presented new axioms for singquandles, simplified existing ones, and reformulated for affine singquandles.

result Simplified applications and revealed new algebraic aspects of singquandles.

singquandles algebraic structure Reidemeister moves singular knots quandles

2021-07-10abs ↗pdf ↗

A G-Family of Singquandles and Invariants of Dichromatic Singular linksmath.GT

New singquandles help distinguish certain types of links.

problem Distinguishing different types of singular links.

method Introduced G-Family of singquandles and used them to define invariants.

result These invariants can distinguish some dichromatic singular links.

singquandles invariants dichromatic links singular links

2023-01-10abs ↗pdf ↗

Singquandles, Psyquandles and Singular Knots: A Surveymath.GT

Survey of algebraic structures for singular knots.

problem Invariants of singular knots using quandle-like structures.

method Exploration of singquandles, psyquandles, and their invariants.

result Enhancements to the singquandle counting invariant and new polynomial invariants.

singular knots quandles psyquandles invariants

2021-03-09abs ↗pdf ↗

Singquandle Shadows and Singular knot Invariantsmath.GT

New invariants for singular knots and links defined using shadow structures.

problem Defining invariants for singular knots and links.

method Introducing action of singquandles on sets and defining shadow counting and polynomial invariants.

result Enhanced shadow counting invariant for singular knots and links.

singular knot theory shadow structures invariants singquandle action polynomial invariant

2021-01-21abs ↗pdf ↗

Cocycle Invariants and Oriented Singular Knotsmath.GT

New invariant distinguishes singular knots and links.

problem Classifying singular knots and links.

method Using oriented singquandles and weight functions at crossings.

result Distinguishes singular granny knot from singular square knot.

cocycle invariant singular knots oriented singquandles weight functions

2020-09-16abs ↗pdf ↗

Singular braids, singular links and subgroups of camomile typemath.GT

The paper defines subgroups of camomile type and studies singular braids and links.

problem Understanding subgroups of camomile type in singular braid groups.

method Presentations, defining relations, and group theory.

result The center of

SG_n

is a direct factor in

SP_n

but not in

SP_n

singular braids singular links subgroups of camomile type finite presentations group theory

2022-12-16abs ↗pdf ↗