This thesis is concerned with the study of the deep connection between the two fundamental notions of de Rham cohomology and differentiable singular cohomology. We develop relevant sheaf theory and notions of cohomology, and show the existence of an axiomatic sheaf cohomology theory via sheaf resolutions. The strength of sheaf co- homology theory lies in that we can prove that sheaf cohomology theories are unique. Furthermore, we determine sheaf resolutions which give rise to sheaf cohomologies that are isomorphic to the classical differentiable singular cohomology and de Rham coho- mology respectively. By uniqueness we assert that the cohomologies are isomorphic, with the principal ideal domain being the field of real numbers. The de Rham theorem determines the isomorphism, and we conclude that, though they are concerned with differential forms, the de Rham cohomology groups are topological invariants.
Date of Award28 Aug 2018
Original languageEnglish
Awarding Institution
  • University of Copenhagen
SupervisorHans Plesner Jakobsen (Supervisor)


  • Sheaf Theory
  • Differential Geometry
  • Topology
  • Cohomology
  • Axiomatic Sheaf Theory
  • Sequences
  • Cochain Complexes

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