On fundamental groups of quotient spaces

Jack S. Calcut
Department of Mathematics
Oberlin College
Oberlin OH 44074

Robert E. Gompf
Department of Mathematics
University of Texas at Austin
1 University Station C1200
Austin, TX 78712-0257

John D. McCarthy
Department of Mathematics
Michigan State University
E. Lansing, MI 48824-1027

September 22, 2011

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