Subject: fundamental group family From: Kirsten Wickelgren Date: Wed, 12 Sep 2007 20:44:41 -0700 Hello all, Ravi Vakil and I were wondering if anyone had an opinion about the name of the following object: given a space X, pi_1(X,x) varies continuously with x and one can glue the pi_1(X,x) together to form a group object over X whose fibers are pi_1(X,x). Does this have a standard name? We've been calling it by names like the fundamental group family, the fundamental group bundle, the relative fundamental group, and the fundamental relative group. Opinions? Thank you, Kirsten Wickelgren