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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).

6 votes
2 answers
321 views

On trivalent spines of surfaces

Let $\Sigma$ be a surface with non-empty boundary labelled by finitely many points $x_i$. For our purposes a spine $s$ for $\Sigma$ is a uni-trivalent graph embedded in $\Sigma$ whose 1-vertices are p …
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6 votes
1 answer
241 views

Does there always exist a sequence of handle moves between handle decompositions that does n...

Reference request: Firstly, I'm looking for a proof of the following well-known result about handle decompositions: ($\ast$) Given two handle decompositions of a smooth $n$-manifold $M$, there exi …
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  • 365