Research ArticleNo Access

The non-orientable 4-genus of 11 crossing non-alternating knots

Department of Mathematics, Louisiana State University, USA

https://doi.org/10.1142/S0218216524500500Cited by:0 (Source: Crossref)

Abstract

The non-orientable 4-genus of a knot $K$ $K$ in $S^{3}$ $S^{3}$ is defined to be the minimum first Betti number of a non-orientable surface $F$ $F$ smoothly embedded in $B^{4}$ $B^{4}$ so that $K$ $K$ bounds $F$ $F$ . We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots. We will also view obstructions to a knot bounding a Möbius band given by the double branched cover of $S^{3}$ $S^{3}$ branched over $K$ $K$ .

Keywords:

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