synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
(shape modality $\dashv$ flat modality $\dashv$ sharp modality)
$(\esh \dashv \flat \dashv \sharp )$
dR-shape modality$\dashv$ dR-flat modality
$\esh_{dR} \dashv \flat_{dR}$
(reduction modality $\dashv$ infinitesimal shape modality $\dashv$ infinitesimal flat modality)
$(\Re \dashv \Im \dashv \&)$
fermionic modality$\dashv$ bosonic modality $\dashv$ rheonomy modality
$(\rightrightarrows \dashv \rightsquigarrow \dashv Rh)$
Models
Models for Smooth Infinitesimal Analysis
smooth algebra ($C^\infty$-ring)
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
A statement about sufficient data for extensions of a smooth function from a compact subset to an open neighbourhood.
extension theorems | continuous functions | smooth functions |
---|---|---|
plain functions | Tietze extension theorem | Whitney extension theorem |
equivariant functions | equivariant Tietze extension theorem |
The original article is
Textbook accounts include
Enhancement to a linear splitting of restriction maps on Fréchet spaces of sections with compact support of vector bundles:
This is then used to show the restriction map to (suitable) regular closed subsets is a submersion of mapping spaces (with maps valued in an arbitrary manifold).
See also
Wikipedia, Whitney extension theorem
Armin Rainer, Ultradifferentiable extension theorems: a survey, Expositiones Mathematicae (2021) [arXiv:2107.01061, doi:10.1016/j.exmath.2021.12.001]
Last revised on June 30, 2022 at 19:55:45. See the history of this page for a list of all contributions to it.