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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

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A (not existing) self-homeomorphism of the figure eight knot complement

I was recently looking at the figure eight knot complement $M$, as a once-punctured torus bundle over the surface with monodromy $ A=\begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix} $ and its sister with …
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