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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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Covariant derivative of determinant of the metric tensor

The determinant of a metric makes perfectly good sense, but it is not a function, rather a $2$-density. Formally, this means that it transforms as a section of the bundle associated with the frame bun …
Dan Fox's user avatar
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