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Abstract
We describe 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 cohomology 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 cohomology respectively. By uniqueness we assert that the cohomologies are isomorphic, with the principal ideal domain set to 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.
Original language  English 

Number of pages  1 
Publication status  Published  18 Oct 2022 
Event  NVD 50 ár  Kongshøll, Vestara bryggja, Tórshavn, Faroe Islands Duration: 18 Nov 2022 → 18 Nov 2022 
Exhibition
Exhibition  NVD 50 ár 

Country/Territory  Faroe Islands 
City  Tórshavn 
Period  18/11/22 → 18/11/22 
Keywords
 Sheaf Theory
 Differential Geometry
 Topolgy
 Cohomology
 Axiomatic Sheaf Theory
 Sequences
 Cochain Complexes
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NVD 50 ár
Abrahamsen, H. (Organiser), á Fríðriksmørk Berbisá, M. (Organiser), Beyer, H.G. (Organiser), Blaasvær, H. F. E. (Organiser), Christiansen, S. (Organiser), Djurhuus, A. (Organiser), Gislason, H. (Organiser), Halling, J. (Organiser), í Hjøllum, J. (Organiser), Joensen, B. (Organiser), Joensen, H. P. (Organiser), í Kongsstovu, S. K. (Organiser), Kristmundsson, J. (Organiser), Magnussen, E. (Organiser), Mikalsen, S.O. (Organiser), Simonsen, H. (Organiser), Simonsen, K. (Organiser), Svøðstein, J. (Organiser), Thomsen, M. J. (Organiser) & Xin, Q. (Organiser)
18 Nov 2022Activity: Participating in or organising an event › Organising a conference, workshop, ...