In recent work (beginning with [8]) Kronhcimcr and Mrowka have developed the formidable machinery of "gauge theory for embedded surfaces", and deployed it against a host of problems of the general form, "What is the least genus of a .smooth surface representing a specified homology class in a given 4-manlfold?" One of their results (the "local Thorn Conjecture") can be used [19] to derive a lower bound (the "slicc-Benncquin inequality", hereinafter sBi) for the Murusuqi (or slice) genus of a knot K∈S3- that is, the smallest genus of a smooth, oriented surface in DA with boundary K. A knot is slice if it has Murasugi genus 0, no in particular sBi provides an obstruction to sliceness.
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