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arXiv:1305.4215 [math.AT]AbstractReferencesReviewsResources

Homomorphims from the fundamental group of planar sets

Curt Kent

Published 2013-05-18, updated 2015-11-04Version 2

We prove that every homomorphism from the fundamental group of a planar Peano continuum to the fundamental group of a planar or one-dimensional Peano continuum is induced by a continuous map up to conjugation. This is then used to provide a family of uncountable many planar Peano continua with pairwise non-isomorphic fundamental groups all of which are not homotopy equivalent to a one-dimensional space.

Comments: This is a short note showing how to extend a previous paper by the author and Greg Conner to the planar setting
Categories: math.AT, math.GT
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