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Geometry: Difference between revisions
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Each section corresponds to a video in the lecture series below. The pedagogy follows a conceptual stack of layered mathematical structure from first principles. The initial utility of this page is that it will ideally allow for a user to ctrl-f any technical term and find out: | Each section corresponds to a video in the lecture series below. The pedagogy follows a conceptual stack of layered mathematical structure from first principles. The initial utility of this page is that it will ideally allow for a user to ctrl-f any technical term and find out: | ||
# at what point it lies in the stack | # at what point it lies in the stack | ||
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proof of the equivalence of local sections and G-equivariant functions; linear actions on associated vector fibre bundles; matrix Lie group; construction of the covariant derivative for local sections on the base manifold. | proof of the equivalence of local sections and G-equivariant functions; linear actions on associated vector fibre bundles; matrix Lie group; construction of the covariant derivative for local sections on the base manifold. | ||
==Applications== | ==Applications== | ||
===Quantum mechanics on curved spaces=== | ===Quantum mechanics on curved spaces=== | ||
[https://www.youtube.com/watch?v=C93KzJ7-Es4&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=26 Lecture 26] | [https://www.youtube.com/watch?v=C93KzJ7-Es4&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=26 Lecture 26] | ||
===Spin structures=== | ===Spin structures=== | ||
[https://www.youtube.com/watch?v=Way8FfcMpf0&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=27 Lecture 27] | [https://www.youtube.com/watch?v=Way8FfcMpf0&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=27 Lecture 27] | ||
===Kinematical and dynamical symmetries=== | ===Kinematical and dynamical symmetries=== | ||
[https://www.youtube.com/watch?v=F3oGhXNhIDo&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=28 Lecture 28] | [https://www.youtube.com/watch?v=F3oGhXNhIDo&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=28 Lecture 28] | ||
{{Stub}} | |||
[[Category:Graph, Wall, Tome]] | [[Category:Graph, Wall, Tome]] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||