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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.

168,657 papers · 148 categories

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3 results for “6-cycles”

On spherical Deligne complexes of type

D_n

math.GR

Artin groups of type $D_n$ have special cycles and complexes with interesting properties.

problem Characterizing cycles and complexes in Artin groups of type

D_n

method Analyzing 6-cycles and their centers/quasi-centers in the 1-skeleton of the Artin complex.

result Certain 6-cycles in the Artin complex of type

D_n

have centers or quasi-centers.

Artin groups spherical Deligne complex 6-cycles centers quasi-centers

2024-05-18abs ↗pdf ↗

Cycles in spherical Deligne complexes and application to

K(π,1)

-conjecture for Artin groupsmath.GR

New method finds large curved subcomplexes, proving conjectures for specific groups.

problem Proving the K(π,1)-conjecture for Artin groups.

method Finding large non-positively curved subcomplexes in spherical Deligne complexes.

result Proves K(π,1)-conjecture for many Artin groups, except one.

Artin groups Deligne complexes K(π 1)-conjecture non-positively curved

2024-05-20abs ↗pdf ↗

Crossing numbers and rotation numbers of cycles in a plane immersed graphmath.GT

Odd crossing numbers and even rotation numbers for cycles in plane immersions.

problem Analyzing crossing and rotation numbers of cycles in plane immersions of graphs.

method Generic immersions and Legendrian embeddings of graphs, focusing on cycles of specific lengths.

result Sum of rotation numbers of all 5-cycles is even, and sum of crossing numbers is odd.

crossing numbers rotation numbers immersions cycles graphs

2022-05-02abs ↗pdf ↗