A geometry theory of wild arcs
Date
1974
Authors
Hemion, Geoffrey John
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Abstract
A topological embedding of a I-cell in the 3-sphere is
called an arc. Arcs which are wild at a single point have been
the subject of a number of studies over the past twenty five years.
They have proven to be interesting in their own right as well as
being sources for examples of topological embeddings in 3-manifolds.
This thesis is devoted to a characterization of arcs which
are wild at a single point, at which they have finite penetration
index, in terms of sequences of tame sets. In order to do this
the notion of a "prime" arc is defined and a unique prime
decomposition theorem is proved. The prime arcs have the property
that "levels" of "echelon neighbourhoods", which are 3-cells
surrounding the wild point, can be defined. The characterization
involves studying these levels.
If the penetration index is three the characterization
becomes particularly easy and Chapter 6 is devoted to a description
of arcs of penetration index three.
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