Article ID Journal Published Year Pages File Type
4657891 Topology and its Applications 2016 15 Pages PDF
Abstract

We introduce the right homotopy shift of paths and loops in the inverse limit of a single upper semi-continuous multivalued function on the unit interval. Consequently we obtain a shift in the fundamental group, which turns out to be an injective map under conditions usually assumed for such one-dimensional limits. As a result we obtain strong restriction on the fundamental groups of such inverse limits: they are not finitely generated and are often trivial or uncountable.

Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
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