Schreiber Cosimplicial C-infinity rings and the de Rham complex of Euclidean space

This is one result from Stel's master thesis:

• Herman Stel, Cosimplicial $C^\infty$ rings and the de Rham complex of Euclidean space (arXiv:1310.7407)

showing that under the Dold-Kan correspondence the cosimplicial algebra of functions of the infinitesimal singular simplicial complex is isomorphic to the de Rham complex.

In (dcct, 4.5.1.3) is discussed how this serves to embed Lie algebroids into synthetic differential ∞-groupoids.

Related projects

• differential cohomology in a cohesive topos

  • Synthetic Quantum Field Theory

    • Quantum gauge field theory in Cohesive homotopy type theory

  • cohomology

    • Principal ∞-bundles – models and general theory

    • Fivebrane structures

    • Cosimplicial $C^\infty$ rings and the de Rham complex of Euclidean space

  • ∞-Chern-Weil theory

    • L-∞ algebra connections

    • Cech cocycles for differential characteristic classes

    • Twisted differential structures

      • Twisted Differential String and Fivebrane Structures

      • The moduli 3-stack of the C-field

  • ∞-Chern-Simons theory

    • A higher stacky perspective on Chern-Simons theory

    • Higher Chern-Weil Derivation of AKSZ Sigma-Models

    • 7d Chern-Simons theory and the 5-brane

    • Extended higher cup-product Chern-Simons theories

  • ∞-Wess-Zumino-Witten theory

    • The brane bouquet

    • Obstruction theory for parameterized higher WZW terms

  • Higher geometric prequantum theory

    • Classical field theory via Cohesive homotopy types

    • Local prequantum field theory

    • L-∞ algebras of local observables from higher prequantum bundles

    • Higher extensions of mapping class groups

  • Motivic quantization of local prequantum field theory

    • Geometric quantization of symplectic and Poisson manifolds

    • Cohomological quantization of local prequantum boundary field theory