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

The non-orientable 4-genus of a knot K in S3 is defined to be the minimum first Betti number of a non-orientable surface F smoothly embedded in B4 so that K bounds 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 M & ouml;bius band given by the double branched cover of S3 branched over K.