On fundamental groups of quotient spaces
Jack S. Calcut, Robert E. Gompf, and John D. McCarthy

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Topics in Algebra
