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is a 2-disk with genus 0.) There can be an arbitrarily great difference between the smooth and the topologically locally flat slice genus of a knot; a theorem of
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Charles, A survey of classical knot concordance, in:
325:"The slice genus and the Thurston-Bennequin invariant of a knot"
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is 1, then the topologically locally flat slice genus of
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The (smooth) slice genus is zero if and only if the knot is
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is 0, but it can be proved in many ways (originally with
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is required to be smoothly embedded, then this integer
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273:{\displaystyle g_{s}(K)\geq ({\rm {TB}}(K)+1)/2.\,}
175:is 1 while the genus and the smooth slice genus of
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330:Proceedings of the American Mathematical Society
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190:is bounded below by a quantity involving the
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171:such that the Alexander polynomial of
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186:The (smooth) slice genus of a knot
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192:Thurston–Bennequin invariant
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62:properly embedded in the 4-ball
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344:10.1090/S0002-9939-97-04258-5
311:Milnor conjecture (topology)
117:topologically locally flatly
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363:Handbook of knot theory
115:is required only to be
46:) is the least integer
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38:(sometimes called its
16:Concept in mathematics
323:Rudolph, Lee (1997).
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89:and is often denoted
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149:Alexander polynomial
403:knot theory-related
369:, Amsterdam, 2005.
73:More precisely, if
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167:there exist knots
83:smooth slice genus
461:Knot theory stubs
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25:slice genus
21:mathematics
450:Categories
306:knot genus
301:Slice knot
285:concordant
50:such that
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58:of genus
367:Elsevier
295:See also
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