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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