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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).

1 vote
1 answer
834 views

Handle slides homeomorphism

For handle decomposition of surface, suppose I have a twisted 1-handle(twisted only once) adjacent to an isolated pair of linked handles, is the handle slide operation enough to move the previous one …
Hu Yi Chen's user avatar
8 votes
3 answers
2k views

Whitehead doubles of any knots

I was curious about the fact that the Whitehead doubles of all knots have Alexander polynomial equal to 1, which is the same as a unknot. How to prove this?
Hu Yi Chen's user avatar