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

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4 results for “multicrossings”

Virtual Multicrossings and Petal Diagrams for Virtual Knots and Linksmath.GT

Virtual knots and links get multicrossings and petal diagrams.

problem Defining multicrossings for virtual knots and links.

method Extending multicrossings to virtual knots and links, showing petal diagrams exist.

result Petal diagrams exist for all virtual knots.

virtual knots virtual links multicrossings petal diagrams

2021-03-15abs ↗pdf ↗

From integrals to combinatorial formulas of finite type invariants -- a case studymath.GT

New formula for knot invariants simplifies calculations and counts.

problem Calculating knot invariants for various diagrams.

method Localized configuration space integral with a new Gauss form.

result Yields arrow diagram expressions and new lower bounds.

knot invariants arrow diagrams configuration space Casson invariant multicrossing knots

2022-12-24abs ↗pdf ↗

A New Bound on Odd Multicrossing Numbers of Knots and Linksmath.GT

New bounds on odd multicrossing numbers of knots and links are established.

problem Determining bounds on the number of crossings in knots and links.

method Proved inequalities involving the

(2k+1)

-crossing number, 3-genus, and number of components of a link.

result Established new bounds on the odd crossing numbers of torus knots and links.

knot theory link theory crossing numbers genus torus knots

2020-10-29abs ↗pdf ↗

The crossing and the arc from the topological viewpointmath.GT

The paper describes topological properties of arcs and crossings in knot theory.

problem Understanding the topological nature of arcs and crossings in knot theory.

method Topological description of arcs and crossings as isotopy classes of probes, homotopy classes of diagram elements.

result Sets of arcs and crossings are fundamental for algebraic objects like quandles, partial ternary quasigroups, biquandloids, and crossoids.

knot theory topology quandles partial ternary quasigroups biquandloids

2025-04-26abs ↗pdf ↗