Lie group

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ADE classification

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The universal compact lie group is the topological monoid \(L({\mathbf{R}}^\infty, {\mathbf{R}}^\infty)\) of linear isometric self-embeddings?

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symplectic

- Tags: - #todo/learning/definitions #projects/notes/reading #projects/my-talks #geomtop/symplectic-topology #MOC - Refs: - Crash course in manifolds: https://people.maths.ox.ac.uk/ritter/lie-groups/Ritter-Lie-Groups-HT2015.pdf#page=5 #resources/notes - Mike’s course notes #resources/notes/lectures - Harvard Course Notes 2021 #resources/notes/lectures - Cannas da Silva Lectures on Symplectic Geometry #resources/books - Links to physics: https://people.maths.ox.ac.uk/ritter/ritter-survey-2.pdf#page=1 #resources/notes - Hutchings’ course: https://web.ma.utexas.edu/users/vandyke/notes/242_notes/ #resources/full-courses - Links: - Talbot Talk 2 - Lie group
orbifold

Special case: quotient spaces \(M/G\) for \(G\) a compact Lie group acting smoothly on a smooth manifold. In this case \({ { {H}^{\scriptscriptstyle \bullet}} }(M/G) \cong { { {H}^{\scriptscriptstyle \bullet}} }_G(M)\), where the first is orbifold cohomology and the second is \(G{\hbox{-}}\)equivariant homology.
Lie algebra

- Tags: - #lie-theory - Refs: - #todo/add-references - Links: - Lie group - Coxeter number - adjoint representation - Weight/root theory: - Unsorted/highest weight - dominant weight - fundamental weights - weight lattice - root
2021-04-26_Cohomology_of_SOn

Lie group