Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-10-05
Int.J.Theor.Phys. 41 (2002) 1857-1902
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
48 pages, last, extended and further corrected version; to appear in the October (2002) issue of the International Journal of
Scientific paper
The present paper is a continuation of our work on curved finitary spacetime sheaves of incidence algebras and treats the latter along Cech cohomological lines. In particular, we entertain the possibility of constructing a non-trivial de Rham complex on these finite dimensional algebra sheaves along the lines of the first author's axiomatic approach to differential geometry via the theory of vector and algebra sheaves. The upshot of this study is that important `classical' differential geometric constructions and results usually thought of as being intimately associated with smooth manifolds carry through, virtually unaltered, to the finitary-algebraic regime with the help of some quite universal, because abstract, ideas taken mainly from sheaf-cohomology as developed in the first author's Abstract Differential Geometry theory. At the end of the paper, and due to the fact that the incidence algebras involved have been previously interpreted as quantum causal sets, we discuss how these ideas may be used in certain aspects of current research on discrete Lorentzian quantum gravity.
Mallios Anastasios
Raptis Ioannis
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