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Geometry of Differential Forms Shigeyuki Morita
Publisher: American Mathematical Society

The notion of n -plectic form is a generalization of the notion of symplectic form to differential forms of more than two arguments. Idea; Axiomatics; Models; Well adapted models; Variations. Tangent bundle; Differential equation; Differential forms. I also own a copy of Wald's textbook, as well as Carroll's "Spacetime and Geometry". Unlike MTW it is very much focused on coordinate-dependent calculations, and does not use differential forms. Constructions in synthetic differential geometry. One of the main issues in noncommutative differential geometry is how to define differential forms and vector fields. Now, Kähler differentials have an extremely nice property: they commute with localization. The subtleties are introcuded in matrix geometry ready for more general algebras. For those who have done a bit of differential geometry, this should be looking familiar: it is an algebraic analogue of 1-forms. Higher categorical versions; Supergeometric versions. This is considered in higher symplectic geometry, specifically: in multisymplectic geometry.