Cartan's method and its applications in sheaf cohomology
Algebraic Topology
2023-03-14 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2204.13185,
title = {Cartan's method and its applications in sheaf cohomology},
author = {Yuan Liu},
journal= {arXiv preprint arXiv:2204.13185},
year = {2023}
}