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Corks, covers, and complex curves

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arxiv 2107.06856 v1 pith:5P7DQHLQ submitted 2021-07-14 math.GT math.CVmath.SG

Kyle Hayden This is my paper · ORCID
classification math.GTmath.CVmath.SG
keywords complexcorkscoverscurvesdisksmathbbballbraids
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We show that $\mathbb{C}^2$ contains pairs of properly embedded, smooth complex curves that are isotopic through homeomorphisms but not diffeomorphisms of $\mathbb{C}^2$. The construction is based on realizing corks as branched covers of holomorphic disks in the 4-ball. These disks can also be described using exotic factorizations of quasipositive braids.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Khovanov homology and equivariant surfaces

    math.GT 2025-07 conditional novelty 7.0 of 10

    The Borel refinement of Bar-Natan Khovanov homology detects that equivariant slice genus can be arbitrarily larger than isotopy-equivariant slice genus.

  2. Lecture notes on link homologies and knotted surfaces

    math.GT 2025-07 conditional novelty 2.0 of 10

    Lecture notes presenting the cobordism maps on Khovanov and link Floer homology as invariants of knotted surfaces, with worked examples and exercises.

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