# Details of talk

Title | A missing link in the classification of immersed curves which extend to immersed surfaces? |
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Presenter | Margaret McIntyre (University of Ghana) |

Author(s) | Dr Margaret McIntyre |

Session | n/a |

Time | |

Abstract | 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. |