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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).
5
votes
Criterion for alternation of the linking form
This is not an answer, but too long for a comment, and hopefully of some use.
I believe the theorem you mention should be true for any 5-dimensional Poincaré duality space $X$. You can define the li …
8
votes
Accepted
Essential Klein bottle in simply connected symplectic 4 manifolds
Let $X$ be the algebraic variety over $\mathbb{R}$ obtained from the projective plain $\mathbb{P}^2$ by blowing up one point $P \in \mathbb{P}^2(\mathbb{R})$. Since $X$ is a smooth projective algebrai …