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20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy: Difference between revisions
20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy (edit)
Revision as of 16:02, 24 July 2023
, 24 July 2023→Spinors and Cohomology
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[[File:Penrosetribar.png|thumb|The tribar shown in pieces, embedded into three open sets. The numbered and circled subregions contain duplicate overlapping points and the rules for translating into the other open sets.]] | [[File:Penrosetribar.png|thumb|The tribar shown in pieces, embedded into three open sets. The numbered and circled subregions contain duplicate overlapping points and the rules for translating into the other open sets.]] | ||
=== | === Cohomology === | ||
Cohomology of a smooth manifold can be computed by solving certain differential equations, or by combinatorially approximating the manifold with a cover as shown with the tribar. Further, it plays a necessary role in Penrose's Twistor theory. Both mathematical approaches are demonstrated in the book by Bott and Tu: | Cohomology of a smooth manifold can be computed by solving certain differential equations, or by combinatorially approximating the manifold with a cover as shown with the tribar. Further, it plays a necessary role in Penrose's Twistor theory. Both mathematical approaches are demonstrated in the book by Bott and Tu: | ||
{{BookListing | {{BookListing | ||
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| desc = Differential Forms in Algebraic Topology by Raoul Bott and Loring Tu. | | desc = Differential Forms in Algebraic Topology by Raoul Bott and Loring Tu. | ||
}} | }} | ||
=== Spinors === | |||
Spinors have two main instantiations: the infinitesimal quantity usually in finite dimensions as the value of a vector field at a point, or as the vector field taken over a finite region of space(time). | Spinors have two main instantiations: the infinitesimal quantity usually in finite dimensions as the value of a vector field at a point, or as the vector field taken over a finite region of space(time). | ||
</div> | </div> | ||