Differential Geometry, Lie Theory and Low-Dimensional Topology, Melbourne, Australia, 2016

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Details of talk

TitleA missing link in the classification of immersed curves which extend to immersed surfaces?
PresenterMargaret McIntyre (University of Ghana)
Author(s)Dr Margaret McIntyre
Sessionn/a
Time
Abstract


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Blank studied the problem of extending a normal immersed circle $f$ in the plane
to the immersion of a closed orientable surface with boundary $f$, by defining
combinatorial structures (subwords) in a word assigned to $f$.
In his PhD thesis  on the classification of immersions which are bounded by
curves in surfaces, [2010, Technischen Universitat Darmstadt] Dennis Frisch
replaced the plane with ${\mathbb S}^2$ and introduced a new class of subword
which could account for extension to a  surjective immersion. We provide an
example and demonstrate Frisch's solution. Then using the same immersed circle
$f$, we demonstrate another combinatorial structure in the word assigned to $f$,
the structure of linked negative groups. The existence of such linked negative
groups reopens the problem of finding all possible extensions to a normal
immersed curve in a surface.