Fundamental groups in projective knot theory
Julia Viro
Stony Brook University, USAOleg Viro
Stony Brook University, USA
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Abstract
We relate properties of a link in the projective space to properties of the group : \begin{itemize} \item is isotopic to a projective line if and only if . \item is isotopic to an affine circle if and only if . \item is isotopic to a link disjoint from a projective plane if and only if contains a non-trivial element of order two. \end{itemize} A simple algorithm which finds a system of generators and relations for in terms of a link diagram of is provided.