2016/02/22 by Yehonatan Sella, Sella, Yehonatan · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1602.06674
openalex publication_date 2016/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A classic result states that on any locally contractible and paracompact topological space, singular cohomology and sheaf cohomology are isomorphic. A result by Ramanan claims that the paracompactness assumption may be removed, but Ramanan's proof in fact implicitly relies on the assumption of paracompactness and does not work in the stated generality. This paper gives a modified proof that, in fact, singular cohomology and sheaf cohomology agree on any locally contractible topological space.