Concerning Fundamental Groups of Locally Connected Subsets of the Plane

Details Concerning Fundamental Groups of Locally Connected Subsets of the Plane Concerning Fundamental Groups of Locally Connected Subsets of the Plane

2011-05-02

arxiv.org/abs/1105.0405v1

Mathematics

Algebraic Topology

Scientific paper

We show that every homomorphism from a one-dimensional Peano continuum to a planar Peano continuum is induced by a continuous map up to conjugation. We then prove that the topological structure of the space of points at which a planar Peano continuum is not semi-locally simply connected is determined solely by algebraic information contained in its fundamental group. Furthermore, we demonstrate how to reconstruct the topological structure of the space of points at which a planar Peano continuum is not semi-locally simply connected using only the subgroup lattice of its fundamental group.

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