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
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
(germ-determined -ideal)
For a smooth manifold, an ideal in its C-infinity ring (smooth algebra) of smooth functions is called germ determined if for any such that the germ of at any point in the zero locus of in coincides with the germ of some element of at , then itself belongs to .
Equivalently, germ-determined ideals are precisely those ideals that are closed under (possibly infinite) sums of locally finite families. One can also take sums with coefficients in a partition of unity.
(germ-determined -ring)
A finitely generated C-infinity ring of the form for some smooth manifold and ideal is germ-determined if the ideal is a germ-determined ideal (Def. ).
Eduardo Dubuc, Sur les modèles de la géométrie différentielle synthétique, Cahiers de Topologie et Geometrie Differentielle Vol. XX-3
(1979) (numdam:CTGDC_1979__20_3_231_0)
Eduardo Dubuc, Schemas , “Prepublications de la Universite de Montreal” 80-81 edited by G. Reyes (1980).
Eduardo Dubuc, Schemes, American Journal of Mathematics, John Hopkins University, Vol. 103-4 (1981) (jstor:2374046)
Eduardo Dubuc, Open Covers and Infinitary Operations in C-inf-rings, Cahiers de Topologie et Geometrie Differentielle Vol. XXII-3 (1981) (numdam:CTGDC_1981__22_3_287_0)
Eduardo Dubuc, Integracion de campos vectoriales y Geometria Diferencial Sintetica, Proceedings of the VII Sem. Nac. de Mat., FAMAF, Univ. Nac. de Cordoba (1984). journal volume, pdf
Eduardo Dubuc, Germ representability and Local integration of vector fields in a well adapted model of SDG, Aarhus Univ. Math. Inst. preprint series (1985/1986), published in Journal of Pure and Applied Algebra Vol. 64, (1990) (doi:10.1016/0022-4049(90)90152-8)
Marta Bunge, Eduardo Dubuc, Archimedian Local C-inf-rings and Models of SDG, Cahiers de Topologie et Geometrie Differentielle Vol. XXVII-3 (1986). NUMDAM
Marta Bunge, Eduardo Dubuc, Local concepts in SDG and germ representability, in D. Kueker et al. (ads), Mathematical Logic and Theoretical Computer Science, Lecture Notes in Pure and Applied Mathematics 106, Marcel Dekker (1987)
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