The fundamental groups of subsets of closed surfaces inject into their first shape groups

Details The fundamental groups of subsets of closed surfaces inject into their first shape groups The fundamental groups of subsets of closed surfaces inject into their first shape groups

2005-12-14

arxiv.org/abs/math/0512343v1

Algebr. Geom. Topol. 5 (2005) 1655-1676

Mathematics

Group Theory

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-67.abs.html

Scientific paper

We show that for every subset X of a closed surface M^2 and every basepoint x_0, the natural homomorphism from the fundamental group to the first shape homotopy group, is injective. In particular, if X is a proper compact subset of M^2, then pi_1(X,x_0) is isomorphic to a subgroup of the limit of an inverse sequence of finitely generated free groups; it is therefore locally free, fully residually free and residually finite.

Affiliated with

Also associated with

No associations

Rating

The fundamental groups of subsets of closed surfaces inject into their first shape groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The fundamental groups of subsets of closed surfaces inject into their first shape groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The fundamental groups of subsets of closed surfaces inject into their first shape groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-168771