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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7 results for “BPS-series”

A Cable Knot and BPS-Series IImath.GT

The paper generalizes BPS-series for $(2,2w+1)$ -cabling of figure eight knot.

problem Generalizing BPS-series for

(2,2w+1)

-cabling of figure eight knot.

method Verification through recursion method and conjecture analysis.

result Strong evidence for

q

-holonomic property and formulas for

(3,3w+1)

-cabling.

BPS-series figure eight knot cabling operation q-holonomic property Dehn surgery

2023-03-15abs ↗pdf ↗

Knot lattice homology and

q

-series invariants for plumbed knot complementsmath.GT

New invariant connects knot homology and BPS series for plumbed knot complements.

problem Understanding invariants of plumbed knot complements.

method Introducing an invariant unifying knot lattice homology and BPS series, proving a surgery formula.

result Proved a surgery formula relating the new invariant to the weighted graded root of the surgered 3-manifold.

plumbed knot complements knot lattice homology BPS series surgery formula

2024-03-21abs ↗pdf ↗

Non-Semisimple TQFT's and BPS

q

-Seriesmath.GT

New relation between quantum groups and BPS series.

problem Connecting quantum groups at roots of unity and generic q.

method Proposing and proving a precise relation between invariants.

result Bridging non-semisimple and semisimple TQFTs.

quantum groups BPS series TQFT roots of unity non-semisimple

2021-07-29abs ↗pdf ↗

Flow loops and quantum groupsmath.GT

Paper connects knot invariants and Morse flow loops.

problem Connecting quantum group invariants and Morse flow loops for knot study.

method Defining a two-variable series invariant by counting Morse flow loops in knot complements and proving it agrees with quantum group BPS series.

result Correspondence proven for all braid-homogeneous knots.

knot theory quantum groups Morse flows flow loops BPS series

2026-05-20abs ↗pdf ↗

Root lattices and invariant series for plumbed 3-manifoldsmath.GT

Study series invariants of plumbed 3-manifolds using root lattices.

problem Understanding invariants of plumbed 3-manifolds twisted by root lattices.

method Use formal series to study invariants, decompose

\widehat{Z}(q)

, and compute in specific cases.

result Show that

\widehat{Z}(q)

is unique and decomposes into related series invariant under five Neumann moves.

plumbed 3-manifolds root lattices invariant series BPS series Neumann moves

2024-05-23abs ↗pdf ↗

Lattice cohomology and

q

-series invariants of

3

-manifoldsmath.GT

New invariant unifies two theories of 3-manifolds, recovering quantum invariants.

problem Quantum invariants of 3-manifolds at roots of unity.

method Introduces a unified invariant for negative definite plumbed 3-manifolds.

result 2-variable refinement of the

\widehat Z

-invariant.

3-manifolds quantum invariants lattice cohomology Heegaard Floer homology BPS series

2021-09-29abs ↗pdf ↗

A Cable Knot and BPS-Seriesmath.GT

New series invariant for knots and cables, with robustness and relations.

problem Computing series invariants for complex knots and cables.

method Explicit computation and analysis of satellite knots, including a cable of the figure eight knot.

result First example of a cable knot with more than ten crossings, demonstrating robustness and integrality.

knot theory series invariants cable knots figure eight knot satellite knots

2021-01-27abs ↗pdf ↗