Topology of the Standard Model, I: Fermions

TL;DR

This paper introduces a topological extension of the Harari-Shupe fermion model, explaining fermion generations, conservation laws, and incorporating color through algebraic topology, linking preon number to fundamental charges.

Contribution

It presents a novel topological framework for fermions that explains generation structure, conservation laws, and color in a unified topological context.

Findings

Three fermion generations explained topologically.

Preon number linearly related to charge, weak isospin, and color.

Topological model accounts for observed fermion properties.

Abstract

The Harari-Shupe model for fermions is extended to a topological model which contains an explanation for the observed fact that there are only three generations of fermions. Topological explanations are given for $\beta$-decay and for proton decay predicted in supersymmetry and string theories. An explanation is given for the observed fact that the three generations of fermions have such similar properties. The concept of "color" is incorporated into the model in a topologically meaningful way. Conservation laws are defined and discussed in the context of the algebraic topology of the model, and preon number is proved to be linearly determined by charge, weak isospin, and color.