On fundamental groups of quotient spaces

TL;DR

This paper explores a dual property of quotient maps with connected fibers, extending classical covering space theory to include applications in orbit and leaf spaces, revealing new insights into their fundamental groups.

Contribution

It introduces a dual property for quotient maps with connected fibers, expanding the understanding of fundamental groups beyond classical covering space theory.

Findings

Identifies a dual property for quotient maps with connected fibers.

Applies the theory to orbit spaces of vector fields.

Provides insights into leaf spaces in foliation theory.

Abstract

In classical covering space theory, a covering map induces an injection of fundamental groups. This paper reveals a dual property for certain quotient maps having connected fibers, with applications to orbit spaces of vector fields and leaf spaces in general.