Framed Knotoids and Their Quantum Invariants

DOI10.1007/S00220-022-04382-1arXiv2108.10246MaRDI QIDQ6375849

Wout Moltmaker

Publication date: 23 August 2021

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.

Mathematics Subject Classification ID

Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) Generalized knots (virtual knots, welded knots, quandles, etc.) (57K12)

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