Yuan Liu
Published 2022-04-27Version 1
This paper aims to use Cartan's original method in proving Theorem A and B on closed cubes to provide a different proof of the vanishing of sheaf cohomology over a closed cube if either (i) the degree exceeds its real dimension or (ii) the sheaf is (locally) constant and the degree is positive. In the first case, we can further use Godement's argument to show the topological dimension of a paracompact topological manifold is less than or equal to its real dimension.
Introduction to Sheaf Cohomology
On equivariant Euler-Poincaré characteristic in sheaf cohomology
On the dual of a $P$-algebra and its comodules, with applications to comparison of some Bousfield classes
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