Weighted Fundamental Group

TL;DR

This paper introduces the theory of weighted fundamental groups for weighted simplicial complexes, extending classical topological concepts to incorporate weights and exploring their algebraic properties and applications.

Contribution

It develops the theory of weighted fundamental groups, generalizing the classical fundamental group and adapting key theorems like van Kampen's to the weighted setting.

Findings

Weighted fundamental groups reduce to classical groups when all weights are one.

Weighted versions of van Kampen's theorem are established.

Applications include analysis of algebraic properties like abelianization and lower central series.

Abstract

In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to the usual fundamental group as a special case. We also study weighted versions of classical theorems like van Kampen's theorem. In addition, we also investigate the abelianization, lower central series and applications of weighted fundamental groups.