The non-orientable 4-genus for knots with 8 or 9 crossings

Abstract

The non-orientable 4-genus of a knot in the 3-sphere is defined as the smallest first Betti number of any non-orientable surface smoothly and properly embedded in the 4-ball, with boundary the given knot. We compute the non-orientable 4-genus for all knots with crossing number 8 or 9. As applications we prove a conjecture of Murakami's and Yasuhara's, and give a new lower bound for the slicing number of knot.

Fixed two values of ${\gamma }_4$ arising from a typographical error. Updated references. Added Journal Ref

References in corpus (2)

• Concordance homomorphisms from knot Floer homology
• Alternating links and definite surfaces

Cited by in corpus (4)

• On a Nonorientable Analogue of the Milnor Conjecture
• On the nonorientable four-ball genus of torus knots
• Non-orientable 4-genus of torus knots
• The concordance crosscap number and rational Witt span of a knot