Framed Knotoids and Their Quantum Invariants

Wout Moltmaker

doi:10.1007/s00220-022-04382-1

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arXiv · 2108.10246

Framed Knotoids and Their Quantum Invariants

Wout Moltmaker

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Abstract

We modify the definition of spherical knotoids to include a framing, in analogy to framed knots, and define a further modification that includes a secondary 'coframing' to obtain 'biframed' knotoids. We exhibit topological spaces whose ambient isotopy classes are in one-to-one correspondence with framed and biframed knotoids respectively. We then show how framed and biframed knotoids allow us to generalize quantum knot invariants to a knotoid setting, leading to the construction of general Reshetikhin-Turaev type biframed knotoid invariants.

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Wout Moltmaker. 2021-08-23. Framed Knotoids and Their Quantum Invariants. https://doi.org/10.1007/s00220-022-04382-1

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