On a refinement of the non-orientable 4-genus of Torus knots-Reference-Cited by-同舟云学术

On a refinement of the non-orientable 4-genus of Torus knots

Published:2023-06-21 Issue:22 Volume:10 Page:242-251
ISSN:2330-1511
Container-title:Proceedings of the American Mathematical Society, Series B
language:en
Short-container-title:Proc. Amer. Math. Soc. Ser. B

Author:

Sabloff Joshua

Abstract

In formulating a non-orientable analogue of the Milnor Conjecture on the 4 4 -genus of torus knots, Batson [Math. Res. Lett. 21 (2014), pp. 423–436] developed an elegant construction that produces a smooth non-orientable spanning surface in B 4 B^4 for a given torus knot in S 3 S^3 . While Lobb [Math. Res. Lett. 26 (2019), pp. 1789] showed that Batson’s surfaces do not always minimize the non-orientable 4 4 -genus, we prove that they do minimize among surfaces that share their normal Euler number. We also determine the possible pairs of normal Euler number and first Betti number for non-orientable surfaces whose boundary lies in a class of torus knots for which Batson’s surfaces are non-orientable 4 4 -genus minimizers.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology,Discrete Mathematics and Combinatorics,Analysis,Algebra and Number Theory

Link

https://www.ams.org/bproc/2023-10-22/S2330-1511-2023-00166-X/S2330-1511-2023-00166-X.pdf

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