A C-infinity ring is a set equipped with n-ary operations corresponding to smooth n-ary functions on the real line (satisfying natural axioms). We prove that the cosimplicial abelian group associated to the de Rham complex of Euclidean space has the structure of a cosimplicial C-infinity ring. We also analyse the notio…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
9 results for “C-infinity-rings”
Defines vector fields and differential forms on local C-infinity-ringed spaces.
problem No specific problem stated; focuses on mathematical definitions.
method Defines tangent sheaf, contractions, Lie derivatives, and proves Cartan equations.
result Standard Cartan calculus equations hold for local C-infinity-ringed spaces.
This is a survey of the author's paper arXiv:1001.0023 on "Algebraic Geometry over C-infinity rings". If X is a smooth manifold then the R-algebra C^\infty(X) of smooth functions c : X --> R is a "C-infinity ring". That is, for each smooth function f : R^n --> R there is an n-fold operation Φ_f : C^\infty(X)^n --> C^\i…
Constructs differential forms on -ringed spaces.
problem Developing a theory of differential forms for non-manifold spaces.
method Functorial construction of differential forms on local -ringed spaces.
result Stokes' theorem holds for integrated forms on simplices.
In the model of synthetic differential geometry consisting of sheaves (with respect to open covers) over the opposite category of the category of closed finitely generated C-infinity rings, any morphism from S, the zeroes of the "amazing right adjoint" of dx, to the real line R extends to a morphism from R to R. This s…
The paper proposes a method to compute higher infinitesimals in numerical and symbolic analysis.
problem Computing higher-order derivatives with higher infinitesimals.
method Automatic differentiation in terms of C-infinity rings and Weil algebras.
result A unifying theoretical framework for multivariate higher-order derivatives.
Lie-Rinehart algebras over -rings defined and studied.
problem Defining and studying Lie-Rinehart algebras over -rings.
method Defining Lie-Rinehart algebras over -rings and showing their relationship with Poisson -rings.
result A natural Poisson bracket on the -ring associated with a Lie-Rinehart algebra over a -ring.
This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras for which infinitely differentiable functions can be evaluated on elements. Such…
This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra to define, in particular, the notion of a differential graded algebra in the wo…