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math.GT2026
Counting tangles in coverings of closed 2-orbifolds via ribbon categories
Adam Klukowski
We describe what a typical covering of a closed 2-orbifold looks like on a small scale. Specifically, we prove that a uniformly random covering of degree n contains in expectation…
math.GT2023
Simple closed curves, non-kernel homology and Magnus embedding
Adam Klukowski
We consider the subspace of the homology of a covering space spanned by lifts of simple closed curves. Our main result is the existence of unbranched covers of surfaces where this…