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Integrated differential geometry. Commutative and noncommutative

Hendrik Grundling
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Abstract

For a manifold M we define a structure on the group action of Diff(M) on the smooth functions on M which reduces to the usual differential geometry upon differentiation at zero along the one-parameter groups of Diff(M). This ``integrated differential geometry'' generalises to all group actions on associative algebras, including noncommutative ones, and defines an ``integrated de Rham cohomology,'' which provides a new set of invariants for group actions. We calculate the first few integrated de Rham cohomologies for two examples;- a discrete group action on a commutative algebra, and a continuous Lie group action on a noncommutative matrix algebra.

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Hendrik Grundling. 1994-11-11. Integrated differential geometry. Commutative and noncommutative. https://arxiv.org/abs/hep-th/9411079

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