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Geometry and physics today. (English) Zbl 1111.83019
This essay represents a kind of meta-theoretical comparison study, between different geometrization methods in theoretical physics: the old ones, belonging to classical differential geometry must (in the author’s opinion) be replaced by some new methods, in the framework of “abstract” differential geometry (described as a general gauge theory on topological manifolds and fiber bundles).
83C45Quantization of the gravitational field
81P05General and philosophical topics in quantum theory
83C05Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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[13]Mallios, A. (1998b). Geometry of Vector Sheaves. An Axiomatic Approach to Differential Geometry, Vols. I (Chapts I–V), II (Chapts VI–XI). Kluwer, Dordrecht. [This is still quoted in the text, as VS].
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[16]Mallios, A. (2006) Quantum gravity and ”singularities.” Note Mat. 25, 57–76.
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[19]Mallios, A. and Raptis, I. (2002). Finitary vCech-de Rham cohomology: much ado without cc-smoothness. Ibid. 41, 1857–1992.
[20]Mallios, A. and Raptis, I. (2003). Finitary, causal, and quantal vacuum Einstein gravity. Ibid. 42, 1479–1620.
[21]Mallios, A. and Raptis, I. (2005). C-smooth singularities exposed: Chimeras of the differential spacetime manifold, research monograph (in preparation); gr-qc/0411121.
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