Bousfield Localizations on the Nonmodular Lattice $N_5$

TL;DR

This paper classifies all model category structures on the nonmodular lattice N_5 and explores their relationships through Bousfield localization, using transfer systems from equivariant homotopy theory.

Contribution

It provides a complete description of model structures on N_5 and links them via Bousfield localization, integrating combinatorial and homotopical techniques.

Findings

Complete classification of model category structures on N_5

Description of relationships between structures via Bousfield localization

Application of transfer systems from equivariant homotopy theory

Abstract

We provide a complete description of the model category structures on the nonmodular lattice $N_5$. Furthermore we explain how these model category structures are related to each other via Bousfield localization. This work heavily relies on the use of combinatorical objects from equivariant homotopy theory known as \emph{transfer systems}, and it results in a wealth of interesting interactions between combinatorial and homotopical methods.