Lecture notes presenting the cobordism maps on Khovanov and link Floer homology as invariants of knotted surfaces, with worked examples and exercises.
Corks, covers, and complex curves
1 Pith paper cite this work. Polarity classification is still indexing.
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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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Lecture notes on link homologies and knotted surfaces
Lecture notes presenting the cobordism maps on Khovanov and link Floer homology as invariants of knotted surfaces, with worked examples and exercises.