312 papers in the wider index

Topology

Continuity, homotopy, and the shape of space itself.

Integer sequences Graph theory Number theory Probability Geometry Analysis Logic

In this topic3 papers in the archive

Preprint · Sep 2026

On the graph-theoretic, spectral, and topological analysis of the Seven Bridges of Königsberg

A formal synthesis of the Seven Bridges of Königsberg, Euler's founding result of 1736, carried into modern language: adjacency, incidence, and Laplacian matrix representations give a self-contained proof of impossibility; the full Laplacian spectrum and eigenbasis, Kirchhoff network flows, and the Kirchhoff index quantify structural efficiency; and two bridge additions — the historical Kaiserbrücke of 1905 and a provably minimal two-bridge Eulerisation — are analyzed exactly.

Taha Athar, Tanver Athar61 reads

arXiv:2410.0912

The Hodge conjecture and algebraic cycles

A bridge between differential forms and the cohomology of projective varieties: we verify the Hodge conjecture for a new class of abelian fourfolds with prescribed endomorphism structure.

P. Nakashima, E. Vogel1,204 reads

arXiv:2412.1140

The chromatic filtration of sphere spectra

We compute the first two differentials in the Adams spectral sequence at the prime two and describe the chromatic layers of the sphere spectrum up to the third monochromatic floor.

J. Ferreira, N. Adeyemi733 reads