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

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.