# Ascent sliceness

22 Jul 2019 Rushworth William

We introduce the notion of ascent sliceness of virtual knots. A representative of a virtual knot is an embedding $S^1 \hookrightarrow \Sigma_{g} \times I$, for $\Sigma_g$ a closed connected oriented surface of genus $g$; the virtual knot represented is slice if there exists a pair consisting of a disc $D$ and an oriented $3$-manifold $M$, such that $D \hookrightarrow M \times I$, $\partial M = \Sigma_{g}$, and $\partial D = S^1$ (the image of the embedding)... (read more)

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• GEOMETRIC TOPOLOGY