The slicing number of a knot

Abstract

An open question asks if every knot of 4-genus g_s can be changed into a slice knot by g_s crossing changes. A counterexample is given.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-41.abs.html Version 3: reference to Murakami and Yasuhara added

Cited by in corpus (13)

• Chern-Simons functional, singular instantons, and the four-dimensional clasp number
• Immersed disks, slicing numbers and concordance unknotting numbers
• The geometry of the knot concordance space
• The non-orientable 4-genus for knots with 8 or 9 crossings
• The untwisting number of a knot
• Balanced algebraic unknotting, linking forms, and surfaces in three- and four-space
• Untwisting information from Heegaard Floer homology
• Signature invariants related to the unknotting number
• Rasmussen invariants of Whitehead doubles and other satellites
• On slicing invariants of knots
• Concordance invariants of doubled knots and blowing up
• Unknotting via null-homologous twists and multi-twists
• Some examples related to knot sliceness