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.

168,657 papers · 148 categories

Trend · papers per month

count % of corpus

6 results for “15-vertex”

New examples and partial classification of 15-vertex triangulations of the quaternionic projective planemath.CO

New triangulations of quaternionic projective plane found with various symmetry groups.

problem Classifying triangulations of quaternionic projective plane with 15 vertices.

method Constructing and classifying 15-vertex triangulations with various symmetry groups.

result Exactly 75 triangulations of quaternionic projective plane with 15 vertices and symmetry group of order at least 4.

triangulations quaternionic projective plane symmetry groups 15-vertex classification

2023-11-19abs ↗pdf ↗

Random Simple-Homotopy Theorycs.CG

RSHT algorithm simplifies complex shapes to points.

problem Simplifying complex shapes to points in higher dimensions.

method Combines simplicial collapses and expansions.

result Reduces triangulated d-manifolds to points using RSHT.

simple-homotopy simplicial complexes contractible spaces higher-dimensional bistellar flips

2021-07-21abs ↗pdf ↗

A 15-vertex triangulation of the quaternionic projective planemath.AT

In 1992, Brehm and Kühnel constructed a 8-dimensional simplicial complex $M^8_{15}$ with 15 vertices as a candidate to be a minimal triangulation of the quaternionic projective plane. They managed to prove that it is a manifold "like a projective plane" in the sense of Eells and Kuiper. However, it was not known until …

2016-03-17abs ↗pdf ↗

A minimal triangulation of complex projective plane admitting a chess colouring of four-dimensional simplicesmath.GT

In this paper we construct and study a new 15-vertex triangulation $X$ of the complex projective plane $\CP^2$. The automorphism group of $X$ is isomorphic to $S_4\times S_3$ . We prove that the triangulation $X$ is the minimal by the number of vertices triangulation of $\CP^2$ admitting a chess colouring of four-dimens…

2009-04-27abs ↗pdf ↗

634 vertex-transitive and more than

10^{103}

non-vertex-transitive 27-vertex triangulations of manifolds like the octonionic projective planemath.CO

634 vertex-transitive and over 10^103 non-vertex-transitive 27-vertex triangulations of octonionic projective plane.

problem Constructing and classifying triangulations of the octonionic projective plane.

method Combinatorial construction and analysis of symmetry groups.

result Found 634 vertex-transitive and over 10^103 non-vertex-transitive 27-vertex triangulations.

triangulations octonionic projective plane vertex-transitive non-vertex-transitive symmetry groups

2022-07-18abs ↗pdf ↗

On possible symmetry groups of 27-vertex triangulations of manifolds like the octonionic projective planemath.CO

New triangulations of octonionic projective plane found with restricted symmetry groups.

problem Finding symmetry groups of 27-vertex triangulations of manifolds like the octonionic projective plane.

method Using Smith and Bredon's results on transformation groups to restrict possible symmetry groups.

result List of 26 subgroups of S27 containing all possible symmetry groups of 27-vertex triangulations of manifolds like the octonionic project plane.

triangulations octonionic projective plane symmetry groups Smith theory Bredon's fixed point sets

2023-10-25abs ↗pdf ↗